Fair Value Measurements (Details) - USD ($) $ in Millions	9 Months Ended	12 Months Ended
	Sep. 30, 2024	Dec. 31, 2023
Asset of BSIF and consolidated Funds
Total fair value assets	$ 139.7	$ 98.6
Uncategorized	19.7	17.9
Liabilities of consolidated Funds
Total fair value liabilities	$ (5.8)	(4.1)
Real estate investment funds
Liabilities of consolidated Funds
Term over which the underlying assets are expected to be liquidated by the investees	1 year
Quoted prices in active markets (Level I)
Asset of BSIF and consolidated Funds
Total fair value assets	$ 73.8	65.8
Liabilities of consolidated Funds
Total fair value liabilities	(5.7)	(4.0)
Significant other observable inputs (Level II)
Asset of BSIF and consolidated Funds
Total fair value assets	46.2	14.9
Liabilities of consolidated Funds
Total fair value liabilities	(0.1)	(0.1)
Significant unobservable inputs (Level III)
Asset of BSIF and consolidated Funds
Total fair value assets	0.0	0.0
Liabilities of consolidated Funds
Total fair value liabilities	0.0	0.0
Consolidated Funds
Asset of BSIF and consolidated Funds
Common and preferred stock	25.0	19.0
Derivatives	0.5	0.1
Investments in unconsolidated Funds	71.2	33.9
Liabilities of consolidated Funds
Securities sold short	(5.7)	(4.0)
Derivative liability	(0.1)	(0.1)
Consolidated Funds | Corporate bonds
Asset of BSIF and consolidated Funds
Corporate bonds	45.7	14.8
Consolidated Funds | Quoted prices in active markets (Level I)
Asset of BSIF and consolidated Funds
Common and preferred stock	25.0	19.0
Derivatives	0.0	0.0
Liabilities of consolidated Funds
Securities sold short	(5.7)	(4.0)
Derivative liability	0.0	0.0
Consolidated Funds | Quoted prices in active markets (Level I) | Corporate bonds
Asset of BSIF and consolidated Funds
Corporate bonds	0.0	0.0
Consolidated Funds | Significant other observable inputs (Level II)
Asset of BSIF and consolidated Funds
Common and preferred stock	0.0	0.0
Derivatives	0.5	0.1
Liabilities of consolidated Funds
Securities sold short	0.0	0.0
Derivative liability	(0.1)	(0.1)
Consolidated Funds | Significant other observable inputs (Level II) | Corporate bonds
Asset of BSIF and consolidated Funds
Corporate bonds	45.7	14.8
Consolidated Funds | Significant unobservable inputs (Level III)
Asset of BSIF and consolidated Funds
Common and preferred stock	0.0	0.0
Derivatives	0.0	0.0
Liabilities of consolidated Funds
Securities sold short	0.0	0.0
Derivative liability	0.0	0.0
Consolidated Funds | Significant unobservable inputs (Level III) | Corporate bonds
Asset of BSIF and consolidated Funds
Corporate bonds	0.0	0.0
Consolidated Entity Excluding Consolidated Funds
Asset of BSIF and consolidated Funds
Consolidated Funds total	71.2	33.9
Consolidated Funds total	68.5	64.7
Uncategorized	19.7	17.9
Liabilities of consolidated Funds
Consolidated Funds total	(5.8)	(4.1)
Consolidated Entity Excluding Consolidated Funds | Investments in separate accounts
Asset of BSIF and consolidated Funds
Investments in separate accounts		2.1
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	48.8	44.7
Investments in unconsolidated Funds	48.8	44.7
Consolidated Entity Excluding Consolidated Funds | Investments in unconsolidated Funds
Asset of BSIF and consolidated Funds
Investments in unconsolidated Funds	19.7	17.9
Uncategorized	19.7	17.9
Consolidated Entity Excluding Consolidated Funds | Investment funds subject to longer redemption restrictions
Asset of BSIF and consolidated Funds
Uncategorized	3.4	3.6
Consolidated Entity Excluding Consolidated Funds | Quoted prices in active markets (Level I)
Asset of BSIF and consolidated Funds
Consolidated Funds total	25.0	19.0
Consolidated Funds total	48.8	46.8
Liabilities of consolidated Funds
Consolidated Funds total	(5.7)	$ (4.0)
Investment in equity securities		99.00%
Investments in cash equivalents		1.00%
Consolidated Entity Excluding Consolidated Funds | Quoted prices in active markets (Level I) | Investments in separate accounts
Asset of BSIF and consolidated Funds
Investments in separate accounts		$ 2.1
Consolidated Entity Excluding Consolidated Funds | Quoted prices in active markets (Level I) | Investments related to long-term incentive compensation plans
Asset of BSIF and consolidated Funds
Investments related to long-term incentive compensation plans	48.8	44.7
Consolidated Entity Excluding Consolidated Funds | Quoted prices in active markets (Level I) | Investments in unconsolidated Funds
Asset of BSIF and consolidated Funds
Investments in unconsolidated Funds	0.0	0.0
Consolidated Entity Excluding Consolidated Funds | Significant other observable inputs (Level II)
Asset of BSIF and consolidated Funds
Consolidated Funds total	46.2	14.9
Consolidated Funds total	0.0	0.0
Liabilities of consolidated Funds
Consolidated Funds total	(0.1)	(0.1)
Consolidated Entity Excluding Consolidated Funds | Significant other observable inputs (Level II) | Investments in separate accounts
Asset of BSIF and consolidated Funds
Investments in separate accounts		0.0
Consolidated Entity Excluding Consolidated Funds | Significant other observable inputs (Level II) | 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
Consolidated Entity Excluding Consolidated Funds | Significant other observable inputs (Level II) | Investments in unconsolidated Funds
Asset of BSIF and consolidated Funds
Investments in unconsolidated Funds	0.0	0.0
Consolidated Entity Excluding Consolidated Funds | Significant unobservable inputs (Level III)
Asset of BSIF and consolidated Funds
Consolidated Funds total	0.0	0.0
Consolidated Funds total	0.0	0.0
Liabilities of consolidated Funds
Consolidated Funds total	0.0	0.0
Consolidated Entity Excluding Consolidated Funds | Significant unobservable inputs (Level III) | Investments in separate accounts
Asset of BSIF and consolidated Funds
Investments in separate accounts		0.0
Consolidated Entity Excluding Consolidated Funds | Significant unobservable inputs (Level III) | 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
Consolidated Entity Excluding Consolidated Funds | Significant unobservable inputs (Level III) | Investments in unconsolidated Funds
Asset of BSIF and consolidated Funds
Investments in unconsolidated Funds	$ 0.0	$ 0.0