While I have never used bidformytravel, I have used priceline... The only caution I give is MAKE SURE that you are not going to cancel or change plans. Unlike normal hotel reservations, you CANNOT cancel these! Priceline is not very understanding of the changing world.
So... My only caution make sure that who ever you use has a cancellation policy so that you are not out the price of an entire stay, that you didnt stay
