Question

opposite gender of spinster

Answer 1

"Bachelorette" was famously the term used to refer to female contestants on the old The Dating Game TV show and, more recently, The Bachelorette. In older English, the female counterpart term to "bachelor" was "spinster". However, this has acquired negative connotations and mostly been abandoned.

Answer 2

Bachelor. Spinster is not used a lot these days because it is considered offensive.