Here is a link to the Inter-City bus site. Always be sure to check the 'ALL CITIES' option.

http://www.neredennereye.com/buses/tum-merkezler/

I guess your first bus would be Marmaris to Mugla (1.1/4 hour journey).

Mugla to Antalya would need to be an overnight bus (5 hour journey).

Then Antalya to Manavgat (2 hour journey).

Followed by local Dolmus to Side (15/20 minutes).

I would call at the bus station upon your arrival in Marmaris, and seek their assistance. The staff speak very good English, and would be able to advise you on the best connections and travel times.