Debt Instrument, Interest Coverage Ratio

No definition available.

Name:	bsig_DebtInstrumentInterestCoverageRatio
Namespace Prefix:	bsig_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	instant

- Definition

Percentage points added to the reference rate to compute the variable rate on the debt instrument.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtInstrumentBasisSpreadOnVariableRate1
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Face (par) amount of debt instrument at time of issuance.

+ References

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-Publisher FASB
-Name Accounting Standards Codification
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+ Details

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

- Definition

Contractual interest rate for funds borrowed, under the debt agreement.

+ References

+ Details

Name:	us-gaap_DebtInstrumentInterestRateStatedPercentage
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

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

- Definition

The fee, expressed as a percentage of the line of credit facility, for the line of credit facility regardless of whether the facility has been used.

+ References

No definition available.

+ Details

Name:	us-gaap_LineOfCreditFacilityCommitmentFeePercentage
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount, after unamortized (discount) premium and debt issuance costs, of long-term debt. Includes, but not limited to, notes payable, bonds payable, debentures, mortgage loans and commercial paper. Excludes capital lease obligations.

+ References

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+ Details

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

- Definition

The fair value amount of long-term debt whether such amount is presented as a separate caption or as a parenthetical disclosure. Additionally, this element may be used in connection with the fair value disclosures required in the footnote disclosures to the financial statements. The element may be used in both the balance sheet and disclosure in the same submission.

+ References

No definition available.

+ Details

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

- Definition

Indebtedness divided by net capital.

+ References

No definition available.

+ Details

Name:	us-gaap_RatioOfIndebtednessToNetCapital1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	instant

- Details

Name:	us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel2Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_LineOfCreditMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_CreditFacilityAxis=us-gaap_RevolvingCreditFacilityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_VariableRateAxis=us-gaap_FederalFundsEffectiveSwapRateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_VariableRateAxis=us-gaap_LondonInterbankOfferedRateLIBORMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=bsig_RevolvingCreditFacilityExpiringAugust222022Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_SeniorNotesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=bsig_SeniorNotes4.80due2026Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=bsig_SeniorNotes5.125due2031Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Borrowings and Debt (Details)	Feb. 23, 2021 USD ($)	Sep. 30, 2021 USD ($)	Dec. 31, 2020 USD ($)
Fair Value, Inputs, Level 2
Debt Instrument [Line Items]
Carrying value		$ 394,800,000	$ 394,300,000
Fair value		426,600,000	424,900,000
Line of Credit \| Revolving credit facility
Debt Instrument [Line Items]
Face amount	$ 125,000,000	125,000,000	150,000,000
Leverage ratio	2.5
Interest coverage ratio	4.0
Line of Credit \| Revolving credit facility \| Minimum
Debt Instrument [Line Items]
Commitment fee	0.25%
Line of Credit \| Revolving credit facility \| Maximum
Debt Instrument [Line Items]
Commitment fee	0.375%
Line of Credit \| Revolving credit facility \| Fed Funds Effective Rate Overnight Index Swap Rate
Debt Instrument [Line Items]
Basis spread on variable rate	0.50%
Line of Credit \| Revolving credit facility \| London Interbank Offered Rate (LIBOR)
Debt Instrument [Line Items]
Basis spread on variable rate	1.00%
Line of Credit \| Revolving credit facility \| London Interbank Offered Rate (LIBOR) \| Minimum
Debt Instrument [Line Items]
Basis spread on variable rate	1.50%
Line of Credit \| Revolving credit facility \| London Interbank Offered Rate (LIBOR) \| Maximum
Debt Instrument [Line Items]
Basis spread on variable rate	2.00%
Line of Credit \| Revolving credit facility \| Fair Value, Inputs, Level 2
Debt Instrument [Line Items]
Carrying value		33,000,000.0	0
Fair value		33,000,000.0	0
Line of Credit \| Revolving credit facility \| Revolving Credit Facility Expiring August 22, 2022 \| Fair Value, Inputs, Level 2
Debt Instrument [Line Items]
Carrying value		33,000,000.0	0
Fair value		33,000,000.0	0
Senior notes \| Senior Notes, 4.80%, due 2026
Debt Instrument [Line Items]
Face amount		$ 275,000,000
Stated interest rate		4.80%
Senior notes \| Senior Notes, 4.80%, due 2026 \| Fair Value, Inputs, Level 2
Debt Instrument [Line Items]
Carrying value		$ 273,000,000.0	272,800,000
Fair value		298,000,000.0	298,900,000
Senior notes \| Senior Notes, 5.125%, due 2031
Debt Instrument [Line Items]
Face amount		$ 125,000,000
Stated interest rate		5.125%
Senior notes \| Senior Notes, 5.125%, due 2031 \| Fair Value, Inputs, Level 2
Debt Instrument [Line Items]
Carrying value		$ 121,800,000	121,500,000
Fair value		$ 128,600,000	$ 126,000,000.0