Fair Value Measurements - Summary of the Assets and Liabilities that are Measured at Fair Value on a Recurring Basis (Details) - USD ($) $ in Millions	6 Months Ended	12 Months Ended
	Jun. 30, 2023	Dec. 31, 2022
Asset of BSIF and consolidated Funds
Total fair value assets	$ 56.7	$ 50.3
Derivative Liability, Statement of Financial Position [Extensible Enumeration]	Derivative liabilities at fair value	Derivative liabilities at fair value
Total fair value liabilities	$ (3.7)	$ (2.2)
Investments in unconsolidated funds
Asset of BSIF and consolidated Funds
Uncategorized	$ 4.3	4.2
Minimum | Real estate investment funds
Asset of BSIF and consolidated Funds
Term over which the underlying assets are expected to be liquidated by the investees	1 year
Maximum | Real estate investment funds
Asset of BSIF and consolidated Funds
Term over which the underlying assets are expected to be liquidated by the investees	2 years
Consolidated Funds
Asset of BSIF and consolidated Funds
Common stock	$ 6.5
Derivatives	2.8	1.9
Investments in unconsolidated Funds	9.3	1.9
Derivative Liability	(2.4)	(2.2)
Common Stock	(1.3)
Consolidated Entity Excluding Consolidated Funds
Asset of BSIF and consolidated Funds
Derivative asset Consolidated Funds total	9.3	1.9
Consolidated Funds total	47.4	48.4
Consolidated Funds total	(3.7)	(2.2)
Consolidated Entity Excluding Consolidated Funds | Investments in separate accounts
Asset of BSIF and consolidated Funds
Investments in separate accounts	0.1	4.2
Consolidated Entity Excluding Consolidated Funds | Investments related to long-term incentive compensation plans
Asset of BSIF and consolidated Funds
Investments related to long-term incentive compensation plans	43.0	40.0
Investments in unconsolidated Funds	43.0	40.0
Consolidated Entity Excluding Consolidated Funds | Investments in unconsolidated funds
Asset of BSIF and consolidated Funds
Investments in unconsolidated Funds	4.3	4.2
Uncategorized	4.3	4.2
Consolidated Entity Excluding Consolidated Funds | Investment Funds Subject to Longer Redemption Restrictions
Asset of BSIF and consolidated Funds
Uncategorized	4.2	4.1
Quoted prices in active markets (Level I)
Asset of BSIF and consolidated Funds
Total fair value assets	50.0	44.5
Total fair value liabilities	(1.5)	(0.2)
Quoted prices in active markets (Level I) | Consolidated Funds
Asset of BSIF and consolidated Funds
Common stock	6.5
Derivatives	0.4	0.3
Derivative Liability	(0.2)	(0.2)
Common Stock	(1.3)
Quoted prices in active markets (Level I) | Consolidated Entity Excluding Consolidated Funds
Asset of BSIF and consolidated Funds
Derivative asset Consolidated Funds total	6.9	0.3
Consolidated Funds total	43.1	44.2
Uncategorized	4.3	4.2
Consolidated Funds total	$ (1.5)	$ (0.2)
Investment in equity securities	100.00%	100.00%
Quoted prices in active markets (Level I) | Consolidated Entity Excluding Consolidated Funds | Investments in separate accounts
Asset of BSIF and consolidated Funds
Investments in separate accounts	$ 0.1	$ 4.2
Quoted prices in active markets (Level I) | Consolidated Entity Excluding Consolidated Funds | Investments related to long-term incentive compensation plans
Asset of BSIF and consolidated Funds
Investments related to long-term incentive compensation plans	43.0	40.0
Quoted prices in active markets (Level I) | Consolidated Entity Excluding Consolidated Funds | Investments in unconsolidated funds
Asset of BSIF and consolidated Funds
Investments in unconsolidated Funds	0.0	0.0
Significant other observable inputs (Level II)
Asset of BSIF and consolidated Funds
Total fair value assets	2.4	1.6
Total fair value liabilities	(2.2)	(2.0)
Significant other observable inputs (Level II) | Consolidated Funds
Asset of BSIF and consolidated Funds
Common stock	0.0
Derivatives	2.4	1.6
Derivative Liability	(2.2)	(2.0)
Common Stock	0.0
Significant other observable inputs (Level II) | Consolidated Entity Excluding Consolidated Funds
Asset of BSIF and consolidated Funds
Derivative asset Consolidated Funds total	2.4	1.6
Consolidated Funds total	0.0	0.0
Consolidated Funds total	(2.2)	(2.0)
Significant other observable inputs (Level II) | Consolidated Entity Excluding Consolidated Funds | Investments in separate accounts
Asset of BSIF and consolidated Funds
Investments in separate accounts	0.0	0.0
Significant other observable inputs (Level II) | Consolidated Entity Excluding Consolidated Funds | Investments related to long-term incentive compensation plans
Asset of BSIF and consolidated Funds
Investments related to long-term incentive compensation plans	0.0	0.0
Significant other observable inputs (Level II) | Consolidated Entity Excluding Consolidated Funds | Investments in unconsolidated funds
Asset of BSIF and consolidated Funds
Investments in unconsolidated Funds	0.0	0.0
Significant unobservable inputs (Level III)
Asset of BSIF and consolidated Funds
Total fair value assets	0.0	0.0
Total fair value liabilities	0.0	0.0
Significant unobservable inputs (Level III) | Consolidated Funds
Asset of BSIF and consolidated Funds
Common stock	0.0
Derivatives	0.0	0.0
Derivative Liability	0.0	0.0
Common Stock	0.0
Significant unobservable inputs (Level III) | Consolidated Entity Excluding Consolidated Funds
Asset of BSIF and consolidated Funds
Derivative asset Consolidated Funds total	0.0	0.0
Consolidated Funds total	0.0	0.0
Consolidated Funds total	0.0	0.0
Significant unobservable inputs (Level III) | Consolidated Entity Excluding Consolidated Funds | Investments in separate accounts
Asset of BSIF and consolidated Funds
Investments in separate accounts	0.0	0.0
Significant unobservable inputs (Level III) | Consolidated Entity Excluding Consolidated Funds | Investments related to long-term incentive compensation plans
Asset of BSIF and consolidated Funds
Investments related to long-term incentive compensation plans	0.0	0.0
Significant unobservable inputs (Level III) | Consolidated Entity Excluding Consolidated Funds | Investments in unconsolidated funds
Asset of BSIF and consolidated Funds
Investments in unconsolidated Funds	$ 0.0	$ 0.0