<SUBMISSION>
<ACCESSION-NUMBER>0001209191-20-041935
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<PUBLIC-DOCUMENT-COUNT>1
<PERIOD>20190702
<FILING-DATE>20200709
<DATE-OF-FILING-DATE-CHANGE>20200709
<REPORTING-OWNER>
<OWNER-DATA>
<CONFORMED-NAME>DONNELLEY FINANCIAL SOLUTIONS 06/FA
<CIK>0000899243
<STATE-OF-INCORPORATION>TX
<FISCAL-YEAR-END>1231
</OWNER-DATA>
<FILING-VALUES>
<FORM-TYPE>4
<ACT>34
<FILE-NUMBER>001-05842
<FILM-NUMBER>201020406
</FILING-VALUES>
<BUSINESS-ADDRESS>
<STREET1>1015 SOUTH SHEPHERD DRIVE
<CITY>HOUSTON
<STATE>TX
<ZIP>77019
<PHONE>404.367.3827
</BUSINESS-ADDRESS>
<MAIL-ADDRESS>
<STREET1>1201 WEST PEACHTREE STREET
<STREET2>SUITE 2700
<CITY>ATLANTA
<STATE>GA
<ZIP>30309
</MAIL-ADDRESS>
<FORMER-NAME>
<FORMER-CONFORMED-NAME>DFIN SOLUTIONS 06/FA
<DATE-CHANGED>20181127
</FORMER-NAME>
<FORMER-NAME>
<FORMER-CONFORMED-NAME>DONNELLEY FINANCIAL SOLUTIONS 06/FA
<DATE-CHANGED>20161027
</FORMER-NAME>
<FORMER-NAME>
<FORMER-CONFORMED-NAME>DONNELLEY R R & SONS CO 06/FA
<DATE-CHANGED>19930323
</FORMER-NAME>
</REPORTING-OWNER>
<ISSUER>
<COMPANY-DATA>
<CONFORMED-NAME>BOWNE & CO INC
<CIK>0000013610
<ASSIGNED-SIC>2750
<IRS-NUMBER>132618477
<STATE-OF-INCORPORATION>DE
<FISCAL-YEAR-END>1231
</COMPANY-DATA>
<BUSINESS-ADDRESS>
<STREET1>55 WATER STREET
<CITY>NEW YORK
<STATE>NY
<ZIP>10041-0006
<PHONE>2129245500
</BUSINESS-ADDRESS>
<MAIL-ADDRESS>
<STREET1>55 WATER STREET
<CITY>NEW YORK
<STATE>NY
<ZIP>10041-0006
</MAIL-ADDRESS>
</ISSUER>
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<TYPE>4
<SEQUENCE>1
<FILENAME>doc4.xml
<DESCRIPTION>FORM 4 SUBMISSION
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-07-02</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000013610</issuerCik>
        <issuerName>BOWNE &amp; CO INC</issuerName>
        <issuerTradingSymbol>BOB</issuerTradingSymbol>
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    <reportingOwner>
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            <rptOwnerName>DONNELLEY FINANCIAL SOLUTIONS 06/FA</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1500 N. CENTRAL AVE.</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>PHOENIX</rptOwnerCity>
            <rptOwnerState>AZ</rptOwnerState>
            <rptOwnerZipCode>85004</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2019-07-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>20000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1000.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>20000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>21.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-07-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>22.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2019-07-02</value>
            </exerciseDate>
            <expirationDate>
                <value>2029-07-02</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
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                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>35000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes></footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Robert S. Sayasane</signatureName>
        <signatureDate>2019-07-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SUBMISSION>
