Even in places that are not in busy city centers, some hotels booked via Priceline bidding are not able to give rooms with bedding for three people for any of a variety of reasons. Times like this may require comparing the price for two rooms using Priceline, one room using Hotwire or otherwise booking through obviously transparent channels, or just gambling on perhaps someone sleeping on the floor or in a chair.
Of the US hotels I have won via bidding on Priceline, most have been able to give me two double beds when I wanted them so not to have to share a bed.