Hi Jess, i have stayed in Troulos several times but do not know anyone who rents mountain bikes out in the resort. The only chance you may have in Troulos is Victoria rentals. She seems to rent just about everything that is possible to rent so she is worth a try! http://www.skiathosinfo.com/business/victoria-cars.htm
One place i do know that definately hires out mountain bikes is Akropolis rental. They are beside bus stop 4 in Skiathos town.
They do not have a website that i am aware of but their e-mail address is akropoli@otenet.gr
Hope this helps!

John

Thanks very much the Victoria is not far from where we are staying, it'll be worth a try. Many thanks.