Only the first is correct. You don't pay 'for' a bill.

Okay ! First, They have the same meaning, but is a minor nuance between them. - " Pay a bill ", This focuses on the fact that the bill amount should be paid. - " Pay for a bill ", The focus here is on the subject he doing which he's paying for a bill. like you're being asked " What you're doing here ? ", then you answer " I'm paying for a bill ", that means you don't want to mention the bill amount. I hope I helped you.

Pay for : To be punished for doing something bad. Pay: Give money for a service and a product.