Fair Value Measurements - Schedule of Changes in Liabilities Measured at Fair Value on a Recurring Basis (Details) - Contingent Earnout Liabilities - USD ($) $ in Thousands	3 Months Ended	6 Months Ended
Jun. 30, 2026	Jun. 30, 2025	Jun. 30, 2026	Jun. 30, 2025
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period	$ 335,384	$ 48,234	$ 23,293	$ 145,559
Change in fair value of contingent consideration	12,303	(1,957)	14,272	6,104
Fair value of contingent consideration issuances	0	8,766	315,998	8,766
Settlement of contingent consideration	(863)	(38,312)	(6,739)	(143,698)
Balance at end of period	$ 346,824	16,731	$ 346,824	16,731
Contingent earnout liabilities settled through issuance (reduction) of earnout incentive bonus payable		$ 1,500		(1,600)
Contingent earnout liabilities settled through the issuance of related party notes payable included as payments of contingent earnout consideration				$ 5,600

Payment for Contingent Consideration Liability through the settlement of a related party notes payable

No definition available.

Name:	bwin_PaymentForContingentConsiderationLiability
Namespace Prefix:	bwin_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

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

- Definition

Amount of transfers of financial instrument classified as a liability out of level 3 of the fair value hierarchy.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2G
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2G

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-3

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

+ Details

Name:	us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersOutOfLevel3
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of gain (loss) recognized in income from liability measured at fair value on recurring basis using unobservable input (level 3).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-3

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

+ Details

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

- Definition

Amount of issuances of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2G
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2G

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-3

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

+ Details

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

- Definition

Amount of settlements of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-3

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

+ Details

Name:	us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Fair value of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-3

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

+ Details

Name:	us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Details

Name:	us-gaap_FairValueByLiabilityClassAxis=bwin_ContingentEarnoutLiabilitiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: