The page on facebook is called Airport transfers to Fethiye area there are quite a few companies advertising shuttles on that page, there is another one on there called Britishtransfers.com it says shuttles from late Feb early March so you may have some luck with them...
If you put that group name into the search on Facebook and ask to join the group you can check them out and also post asking if there is anyone who wants to share a transfer on the date you are after.
Good luck hope you manage to find something