Miss P,
asiatravel usually offer two types of booking - one type you pay the whole cost of the booking to asiatravel in advance via c/c and the other you pay the hotel on checkout (although you still have to submit your c/c to asiatravel via website when you make booking but they won't access it unless you don't turn up, in which case there will be some charge).
For Bangkok, I know of hotels/apartments that don't ask for c/c when booking via phone.