We stayed in Bridge Bay last year - I don't remember the price - but it was on reservation. Bridge Bay is near Fishing Bridge. If you don't mind dry camping, check and see if Bridge Bay takes your pass. I expect it's cheaper just because it's dry camping. We visited in July and Bridge Bay was full. We tried to add nights and weren't able to even checking every day for cancellations.
But at the end of the day, as others have said, 5 nights at $50 is $250. That is a small price to pay for peace of mind that you have a campsite. And I think Fishing Bridge or Bridge Bay is as centrally located as possible for a park as big as Yellowstone.
