They are generally open till 5pm. If you aren't bothered which bank, then you have several choices.
1. Get off the bus just after the roundabout by the Otogar, there you have Zirrat Bank, TEB and another I can't remember the name of.
2. Get off at the Big Migros and walk down past Migros there is a Garanti Bank & Finans.
3. Go into Fethiye, Iş Bank have a branch opposite the PTT, Garanti & Finans are further up the main street, several other banks have branches on the one way road out of Fethiye.