What is the value of a dollar bill with part of the back printed on the front?

It's not possible to say for sure without seeing your bill, but you may have an "offset error". This mistake is fairly rare and can sell for a couple of hundred dollars, so you should have it examined by a currency dealer.

To explain how this error happens: if a sheet of paper gets stuck and doesn't enter the press, ink is transferred to the other side of the press instead of the paper. When a good sheet finally goes through, it picks up the image it's supposed to plus the image of the opposite side that was transferred to the press cylinder.