We have just done this using Fethiye Lovers. They charged us 400TL for a minibus and driver for the day. The air conditioned bus would have held 8 people.
My tip would be get there as early as possible. We left Calis at 9.30 and the gorge was pretty empty. By the time we left ( about 2.00 ) it was heaving - I had never seen so many people there. The queue for the Ticket Booth must have been at least 20 minutes.
We then went to Yakapark for lunch, but a new discovery for us was that it now served NO ALCOHOL ! Instead we went to Selalepark and had a leisurely lunch in the cool shade of the trees.
Fethiye Lovers were great and it was a brilliant day out for grown ups and kids alike. We looked very smug next to the pickled, fried and scorched Jeep Safaris just arriving from the Carpet Factory .