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Leases - Supplemental Cash Flow Information for Leases (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2025	Dec. 31, 2024	Dec. 31, 2023
Cash paid for amounts included in measurement of lease liabilities:
Operating cash flows used in operating leases	$ 21,775	$ 21,719	$ 19,587
Operating lease non-cash items:
Right-of-use assets obtained in exchange for operating lease liabilities	3,248	2,794	6,414
Right-of-use assets increased through lease modifications and reassessments	$ 2,731	$ 767	$ 1,063

X

- Definition

Right-of-Use Asset Increased from Lease Modifications and Reassessments

+ References

No definition available.

+ Details

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Namespace Prefix:	bwin_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

X

- Definition

Right Of Use Obtained In Exchange For Lease Liability [Abstract]

+ References

No definition available.

+ Details

Name:	bwin_RightOfUseObtainedInExchangeForLeaseLiabilityAbstract
Namespace Prefix:	bwin_
Data Type:	xbrli:stringItemType
Balance Type:	na
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X

- References

No definition available.

+ Details

Name:	us-gaap_CashFlowOperatingActivitiesLesseeAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Amount of cash outflow from operating lease, excluding payments to bring another asset to condition and location necessary for its intended use.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 5
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479041/842-20-45-5

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (g)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-4

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

X

- Definition

Amount of increase in right-of-use asset obtained in exchange for operating lease liability.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 53
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479589/842-20-55-53

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (g)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-4

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Period Type:	duration