
<PAGE>   1

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                       SECURITIES AND EXCHANGE COMMISSION

                             WASHINGTON, D.C. 20549
                            ------------------------

                                 SCHEDULE 14D-1
                             TENDER OFFER STATEMENT
      PURSUANT TO SECTION 14(d)(1) OF THE SECURITIES EXCHANGE ACT OF 1934
                                      AND
                                  STATEMENT ON

                                  SCHEDULE 13D
                   UNDER THE SECURITIES EXCHANGE ACT OF 1934
                            ------------------------

                                COACH USA, INC.
                           (NAME OF SUBJECT COMPANY)

                            STAGECOACH HOLDINGS PLC
                                      AND

                               SCH HOLDINGS CORP.
                                    (BIDDER)
                    COMMON STOCK, PAR VALUE $0.01 PER SHARE
                         (TITLE OF CLASS OF SECURITIES)
                                   18975L106
                     (CUSIP NUMBER OF CLASS OF SECURITIES)

                                 KEITH COCHRANE
                                CHARLOTTE HOUSE
                              20 CHARLOTTE STREET
                                  PERTH PH15LL
                                    SCOTLAND
                          TELEPHONE: +44-1738-442-111
            (NAME, ADDRESS AND TELEPHONE NUMBER OF PERSON AUTHORIZED
           TO RECEIVE NOTICES AND COMMUNICATIONS ON BEHALF OF BIDDER)

                                   COPIES TO:
                            MICHAEL O. WOLFSON, ESQ.
                           99 BISHOPSGATE, 21ST FLOOR
                                LONDON EC2M 3YH
                          TELEPHONE: +44-207-422-4000

                           CALCULATION OF FILING FEE

<TABLE>
<CAPTION>
---------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------
            TRANSACTION VALUATION*                         AMOUNT OF FILING FEE**
<S>                                            <C>
---------------------------------------------------------------------------------------------
                $1,314,470,220                                    $262,895
---------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------
</TABLE>

 * Based on the offer to purchase all of the outstanding shares of Common Stock
   of the Subject Company at a purchase price of $42.00 cash per share,
   25,420,777 shares outstanding, 4,034,645 shares issuable upon the exercise of
   outstanding options, 40,000 shares issuable upon the exercise of outstanding
   warrants, 1,757,845 shares issuable upon conversion of convertible
   subordinated notes outstanding and 63,643 shares issuable in respect of
   certain securities of a subsidiary of the Subject Company.

 ** 1/50 of 1% of Transaction Valuation.

[ ] CHECK BOX IF ANY PART OF THE FEE IS OFFSET AS PROVIDED BY RULE 0-11(a)(2)
    AND IDENTIFY THE FILING WITH WHICH THE OFFSETTING FEE WAS PREVIOUSLY PAID.
    IDENTIFY THE PREVIOUS FILING BY REGISTRATION STATEMENT NUMBER, OR THE FORM
    OR SCHEDULE AND THE DATE OF ITS FILING.

Amount Previously Paid:
Form or Registration No.:
Filing Party:
Date Filed:

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<PAGE>   2

    CUSIP NO. 18975L106

<TABLE>
<S>        <C>                                                          <C>
---------------------------------------------------------------------------

  1        NAMES OF REPORTING PERSONS:
           SCH Holdings Corp.
           S.S. OR I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS:
           76-0608391
---------------------------------------------------------------------------
  2        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (a) [ ]
           (b) [ ]
---------------------------------------------------------------------------
  3        SEC USE ONLY
---------------------------------------------------------------------------
  4        SOURCE OF FUNDS AF
---------------------------------------------------------------------------
  5        CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
           PURSUANT TO ITEM 2(e) OR 2(f) [ ]
---------------------------------------------------------------------------
  6        CITIZENSHIP OR PLACE OF ORGANIZATION Delaware
---------------------------------------------------------------------------
  7        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
           1,499,921*
---------------------------------------------------------------------------
  8        CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (7) EXCLUDES
           CERTAIN SHARES [ ]
---------------------------------------------------------------------------
  9        PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (7)
           5.9% (based on 25,420,777 shares outstanding)
---------------------------------------------------------------------------
  10       TYPE OF REPORTING PERSON CO
---------------------------------------------------------------------------
</TABLE>

---------------

* SCH Holdings Corp., a Delaware Corporation, has entered into a Tender
  Agreement with the directors of Coach USA, Inc., pursuant to which the
  directors have agreed to validly tender (and not withdraw) pursuant to and in
  accordance with the terms of the Offer, all of the Coach USA, Inc. Shares
  beneficially owned by them, and any Shares acquired by them after the date of
  the Tender Agreement.

                                        2
<PAGE>   3

    CUSIP NO. 18975L106

<TABLE>
<S>        <C>                                                          <C>
---------------------------------------------------------------------------
  1        NAMES OF REPORTING PERSONS:
           Stagecoach Holdings plc
           S.S. OR I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS: N/A
---------------------------------------------------------------------------
  2        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (a) [ ]
           (b) [ ]
---------------------------------------------------------------------------
  3        SEC USE ONLY
---------------------------------------------------------------------------
  4        SOURCE OF FUNDS WC and BK
---------------------------------------------------------------------------
  5        CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
           PURSUANT TO ITEM 2(e) OR 2(f) [ ]
---------------------------------------------------------------------------
  6        CITIZENSHIP OR PLACE OF ORGANIZATION Delaware
---------------------------------------------------------------------------
  7        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
           1,499,921*
---------------------------------------------------------------------------
  8        CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (7) EXCLUDES
           CERTAIN SHARES [ ]
---------------------------------------------------------------------------
  9        PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (7)
           5.9% (based on 25,420,777 shares outstanding)
---------------------------------------------------------------------------
  10       TYPE OF REPORTING PERSON CO
---------------------------------------------------------------------------
</TABLE>

---------------

* The footnote on page 2 is incorporated herein by reference.

                                        3
<PAGE>   4

     This Tender Offer Statement on Schedule 14D-1 (this "Statement") relates to
the offer by SCH Holdings Corp., a Delaware corporation ("Purchaser"), to
purchase all of the outstanding shares of Common Stock, par value $0.01 per
share (the "Shares"), of Coach USA, Inc., a Delaware corporation (the
"Company"), at a purchase price of $42.00 per Share, net to the seller in cash,
without interest thereon, upon the terms and subject to the conditions set forth
in the Offer to Purchase dated June 18, 1999 (the "Offer to Purchase"), a copy
of which is attached hereto as Exhibit (a)(1), and in the related Letter of
Transmittal (which, together with the Offer to Purchase, constitute the
"Offer"), a copy of which is attached hereto as Exhibit (a)(2). Purchaser is a
subsidiary of Stagecoach Holdings plc, a public limited company organized under
the laws of Scotland ("Parent"). This Statement also constitutes a Schedule 13D
of Purchaser and Parent.

ITEM 1.  SECURITY AND SUBJECT COMPANY.

     (a) The name of the subject company is Coach USA, Inc. The information set
forth in Section 7 ("Certain Information Concerning the Company") of the Offer
to Purchase is incorporated herein by reference.

     (b) The exact title of the class of equity securities being sought in the
Offer is Common Stock, par value $0.01 per share, of the Company. The
information set forth in the Introduction (the "Introduction") of the Offer to
Purchase is incorporated herein by reference.

     (c) The information set forth in Section 6 ("Price Range of Shares; No Cash
Dividends") of the Offer to Purchase is incorporated herein by reference.

ITEM 2.  IDENTITY AND BACKGROUND.

     (a)-(d) and (g) This Statement is filed by Parent and Purchaser. The
information set forth in Section 8 ("Certain Information Concerning Parent and
Purchaser") of the Offer to Purchase and in Schedule I thereto is incorporated
herein by reference.

     (e) and (f) During the last five years, neither Parent nor Purchaser, nor,
to the best knowledge of Parent or Purchaser, any of the persons listed in
Schedule I to the Offer to Purchase (i) has been convicted in a criminal
proceeding (excluding traffic violations or similar misdemeanors) or (ii) was a
party to a civil proceeding of a judicial or administrative body of competent
jurisdiction and as a result of such proceeding was or is subject to a judgment,
decree or final order enjoining future violations of, or prohibiting activities
subject to, federal or state securities laws or finding any violation of such
laws.

ITEM 3.  PAST CONTACTS, TRANSACTIONS OR NEGOTIATIONS WITH THE SUBJECT COMPANY.

     (a) The information set forth in Section 8 ("Certain Information Concerning
Parent and Purchaser") of the Offer to Purchase is incorporated herein by
reference. Except as set forth in Sections 8 of the Offer to Purchase, since
January 1, 1996, there have been no transactions which would be required to be
disclosed under this Item 3(a) between Parent or Purchaser or, to the best
knowledge of Parent or Purchaser, any of the persons listed in Schedule I to the
Offer to Purchase and the Company or any of its executive offices, directors or
affiliates.

     (b) The information set forth in Section 8 ("Certain Information Concerning
Parent and Purchaser") and Section 10 ("Background of the Offer; Contacts with
the Company"), Section 11 ("The Merger Agreement and Other Agreements") and
Section 12 ("Purpose of the Offer; the Merger; Plans for the Company") of the
Offer to Purchase is incorporated herein by reference. Except as set forth in
Sections 8, 10, 11 and 12 of the Offer to Purchase, since January 1, 1996, there
have been no contacts, negotiations or transactions which would be required to
be disclosed under Item 3(b) between any of Parent and Purchaser or any of their
respective subsidiaries or, to the best knowledge of Parent and Purchaser, any
of those persons listed in Schedule I to the Offer to Purchase and the Company
or its affiliates concerning a merger, consolidation or acquisition, a tender
offer or other acquisition of securities, an election of directors or a sale or
other transfer of a material amount of assets.

                                        4
<PAGE>   5

ITEM 4.  SOURCE AND AMOUNT OF FUNDS OR OTHER CONSIDERATION.

     (a) and (b) The information set forth in Section 9 ("Source and Amount of
Funds") of the Offer to Purchase is incorporated herein by reference.

     (c) Not applicable.

ITEM 5.  PURPOSE OF THE TENDER OFFER AND PLANS OR PROPOSALS OF THE BIDDER.

     (a)-(g) The information set forth in the Introduction, Section 6 ("Price
Range of Shares; No Cash Dividends"), Section 10 ("Background of the Offer;
Contacts with the Company"), Section 11 ("The Merger Agreement and Other
Agreements"), Section 12 ("Purpose of the Offer; the Merger; Plans for the
Company") and Section 14 ("Effect of the Offer on the Market for the Shares, New
York Stock Exchange Listing and Exchange Act Registration") of the Offer to
Purchase is incorporated herein by reference.

ITEM 6.  INTEREST IN SECURITIES OF THE SUBJECT COMPANY.

     (a) The information set forth in the Introduction and Section 8 ("Certain
Information Concerning Parent and Purchaser") of the Offer to Purchase is
incorporated herein by reference. Except as set forth in the Introduction and
Section 8 of the Offer to Purchase, neither Parent nor Purchaser, nor, to the
best knowledge of Parent or Purchaser, any of the persons listed in Schedule I
to the Offer to Purchase or any associate or majority-owned subsidiary of Parent
or Purchaser or any of the persons so listed beneficially owns or has any right
to acquire, directly or indirectly, any Shares.

     (b) The information set forth in the Introduction and Section 11 ("The
Merger Agreement and Other Agreements") of the Offer to Purchase is incorporated
herein by reference. Except as set forth in the Introduction and Section 11 of
the Offer to Purchase, neither Parent nor Purchaser nor, to the best knowledge
of Parent, Purchaser, any of the persons or entities referred to above or any
executive officer, director or subsidiary of any of the foregoing has effected
any transactions in the Shares during the past sixty days.

ITEM 7.  CONTRACTS, ARRANGEMENTS, UNDERSTANDINGS OR RELATIONSHIPS WITH RESPECT
TO THE SUBJECT COMPANY'S SECURITIES.

     The information set forth in the Introduction and Section 9 ("Source and
Amount of Funds"), Section 10 ("Background of the Offer; Contacts with the
Company"), Section 11 ("The Merger Agreement and Other Agreements"), Section 12
("Purpose of the Offer; the Merger; Plans for the Company"), Section 16
("Certain Legal Matters and Regulatory Approvals") and Section 17 ("Fees and
Expenses") of the Offer to Purchase is incorporated herein by reference. Except
as set forth in the Introduction and Sections 9, 10, 11, 12, 16 and 17 of the
Offer to Purchase, Parent and Purchaser, nor, to the best knowledge of Parent or
Purchaser, any of the persons listed in Schedule I to the Offer to Purchase, has
any contract, arrangement, understanding or relationship with any other person
with respect to any securities of the Company (including, but not limited to,
any contract, arrangement, understanding or relationship concerning the transfer
or the voting of any such securities, joint ventures, loans or option
arrangements, puts or calls, guarantees of loans, guarantee agreements or any
giving or withholding of proxies).

ITEM 8.  PERSONS RETAINED, EMPLOYED OR TO BE COMPENSATED.

     The information set forth in the Introduction and Section 17 ("Fees and
Expenses") of the Offer to Purchase is incorporated herein by reference.

ITEM 9.  FINANCIAL STATEMENTS OF CERTAIN BIDDERS.

     The information set forth in Section 8 ("Certain Information Concerning
Parent and Purchaser") of the Offer to Purchase is incorporated herein by
reference.

                                        5
<PAGE>   6

ITEM 10.  ADDITIONAL INFORMATION.

     (a) The information set forth in Section 11 ("The Merger Agreement and
Other Agreements") and Section 12 ("Purpose of the Offer; the Merger; Plans for
the Company") of the Offer to Purchase is incorporated herein by reference.

     (b) and (c) The information set forth in Section 16 ("Certain Legal Matters
and Regulatory Approvals") of the Offer to Purchase is incorporated herein by
reference.

     (d) The information set forth in Section 16 ("Certain Legal Matters and
Regulatory Approvals") of the Offer to Purchase is incorporated herein by
reference.

     (e) None.

     (f) The information set forth in the Offer to Purchase and the Letter of
Transmittal is incorporated herein by reference.

ITEM 11.  MATERIAL TO BE FILED AS EXHIBITS.

     (a)(1) Offer to Purchase dated June 18, 1999.

     (a)(2) Letter of Transmittal.

     (a)(3) Notice of Guaranteed Delivery.

     (a)(4) Letter from the Dealer Manager to Brokers, Dealers, Commercial
Banks, Trust Companies and Nominees.

     (a)(5) Letter to Clients for use by Brokers, Dealers, Commercial Banks,
Trust Companies and Nominees.

     (a)(6) Guidelines for Certification of Taxpayer Identification Number on
Substitute Form W-9.

     (a)(7) Summary Advertisement as published on June 18, 1999.

     (a)(8) Press Release issued by Parent on June 14, 1999.

     (b)(1) Commitment Letter dated June 11, 1999 among Stagecoach Holdings plc,
Credit Suisse First Boston, J.P. Morgan Securities Ltd., The Royal Bank of
Scotland plc and The Governor and Company of The Bank of Scotland.

     (c)(1) Agreement and Plan of Merger dated as of June 12, 1999 among Coach
USA, Inc., SCH Holdings Corp., SCH Acquisition Corp. and Stagecoach Holdings
plc.

     (c)(2) Form of Voting Trust Agreement (filed as Exhibit A to Exhibit
11(c)(1)).

     (c)(3) Tender Agreement dated June 12, 1999 among Stagecoach Holdings plc,
SCH Holdings Corp. and the directors of Coach USA, Inc.

     (c)(4) Employment Term Sheet dated June 12, 1999, executed by Lawrence K.
King, John Mercadante, Jr., Frank Gallagher and Gerald Mercadante and delivered
to Stagecoach Holdings plc.

     (c)(5) Undertaking to Vote, dated June 12, 1999, by Ann Gloag in favor of
Parent and the Company.

     (c)(6) Undertaking to Vote, dated June 12, 1999, by Brain Souter in favor
of Parent and the Company.

     (d) Not applicable.

     (e) Not applicable.

     (f) Not applicable.

                                        6
<PAGE>   7

                                   SIGNATURE

     After due inquiry and to the best of my knowledge and belief, I certify the
information set forth in this Statement is true, complete and correct.

                                          STAGECOACH HOLDINGS PLC

                                          By: /s/ KEITH COCHRANE

                                            ------------------------------------
                                              Name: Keith Cochrane
                                              Title: Group Finance Director

                                          SCH HOLDINGS CORP.

                                          By: /s/ KEITH COCHRANE

                                            ------------------------------------
                                              Name: Keith Cochrane
                                              Title: President

Date: June 18, 1999

                                        7
<PAGE>   8

                                 EXHIBIT INDEX

<TABLE>
<CAPTION>
EXHIBIT                                                                 PAGE
  NO.                             DESCRIPTION                           NO.
-------                           -----------                           ----
<S>       <C>                                                           <C>
11(a)(1)  Offer to Purchase, dated June 18, 1999......................
11(a)(2)  Letter of Transmittal.......................................
11(a)(3)  Notice of Guaranteed Delivery...............................
11(a)(4)  Letter from the Dealer Manager to Brokers, Dealers,
          Commercial Banks, Trust Companies and Nominees..............
11(a)(5)  Letter to Clients for use by Brokers, Dealers, Commercial
          Banks, Trust Companies and Nominees.........................
11(a)(6)  Guidelines for Certification of Taxpayer Identification
          Number on
          Substitute Form W-9.........................................
11(a)(7)  Summary Advertisement as published on June 18, 1999.........
11(a)(8)  Press Release issued by Parent on June 14, 1999.............
11(b)(1)  Commitment Letter dated June 11, 1999 among Stagecoach
          Holdings plc, Credit Suisse First Boston, J.P. Morgan
          Securities Ltd., The Royal Bank of Scotland plc, and The
          Governor and Company of The Bank of Scotland................
11(c)(1)  Agreement and Plan of Merger dated as of June 12, 1999 among
          Coach USA, Inc., SCH Holdings Corp., SCH Acquisition Corp.
          and Stagecoach Holdings plc.................................
11(c)(2)  Form of Voting Trust Agreement (filed as Exhibit A to
          Exhibit 11(c)(1))...........................................
11(c)(3)  Tender Agreement dated June 12, 1999 among Stagecoach
          Holdings plc, SCH Holdings Corp. and the directors of Coach
          USA, Inc....................................................
11(c)(4)  Employment Term Sheet dated June 12, 1999, executed by
          Lawrence K. King, John Mercadante, Jr., Frank Gallagher and
          Gerald Mercadante and delivered to Stagecoach Holdings
          plc.........................................................
11(c)(5)  Undertaking to Vote, dated June 12, 1999, by Ann Gloag in
          favor of Parent and the Company.............................
11(c)(6)  Undertaking to Vote, dated June 12, 1999, by Brain Souter in
          favor of Parent and the Company.............................
</TABLE>

                                        8
