Olympos and Chimera are a lot closer to Antalya than Fethiye. It would probably be easier to hire a car. The route would be the coast road via Kalkan, Kas, Kale and Kumluca. Its quite a pretty coast route and will take about 3.5 to 4 hours from Fethiye.
I am not aware of a Dolmus service from Fethiye, there is only the coastal route bus from Fethiye to Antalya. It does not run very frequently.
Chimera is best seen at night. Climb up there late afternoon or early evening so that you can look around, take some bread and make yourself some toast.Wait for dark to get the full effect. Take a torch for the walk back down.