Even if you requested on priceline bidding, you get what the hotel gives you at check-in. IT IS NEVER GUARANTEE EVEN IF YOU BOOK WITH HOTEL ITSELF AND PAY 2 TIMES MORE.
However, you can call the hotel, if you already won a bid, and ask NICELY that they put down your preference in your reservation record. And call again on the day of your arrival if you are going to be a late check-in, to ask the hotel PLEASE assign you a non-smoking and double bed room.
On the other hand, double bed room actually is less popular than king bed room, and hotel usually assigns less popular room to Priceline customers who paid much less.