High season is August and things get busy then. Otherwise you can find everything from 5 star hotels (with 5 star prices) down to camp sites, all on the beach. Rush can always help you find something. A nearby hotel we have an excellent relationship with is the Yali Han - well worth a look.
For a private house rental try Norman - the author of this page.
I have two adjacent houses in Bitez. One sleeps 6 and the other suits a couple. In the summer I live in one of them and the other may be available for rent.
If you're looking for something really quiet and special for two try Bodrum Garden Cottage. Don't worry about the name. It's only 5 minutes stroll from us. Bodrum
Or book a cheap package holiday to Bitez, Bodrum or Gumbet. You'll need to get the bus from the last two - it'll cost about 80p!