There is a 600 bus which goes from the airport to the otogar, if I remember it was something like silly like a few lira. The 600 goes every half hour. From the otogar there are several services to fethiye. Took about 4 hours including a loo break and was about 18 lira if I remember. It was the Bati something. There are others, ask for the short route. Hope this helps
Not a bad journey at all.