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For Kumluca, based on this website, there are a lot of bus firms that you can use from Antalya (or to Antalya). Mostly used ones are Kamil Koç, Metro Turizm and Pamukkale Turizm. I choose one of these if I were you.
For Kaş, based on this website, there are Metro Turizm, Ulusoy Turizm, Kamil Koç and Pamukkale Turizm which I suggest as well.
You can check their websites and see the bus schedules. These schedules usually won't change based on seasons by the way.