401(k) and Profit Sharing Plan (Details) - USD ($)	12 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Defined Benefit Plan Disclosure [Line Items]
Defined contribution plan, expense recognized	$ 5,800,000	$ 6,200,000	$ 6,500,000
Defined Contribution Plan, Plan Name [Extensible List]	sbh:Plans401KMember
Profit sharing plan, expense recognized	$ 0	$ 0	$ 0
U.S. 401(k) Plan
Defined Benefit Plan Disclosure [Line Items]
Defined Contribution Plan, Plan Name [Extensible List]	sbh:US401KPlanMember
Puerto Rico 401(k) Plan
Defined Benefit Plan Disclosure [Line Items]
Defined Contribution Plan, Plan Name [Extensible List]	sbh:PuertoRico401KPlanMember
Defined Contribution Plan, minimum employment period for contribution to plan	1 year