Here’s what to do, go on this website:
https://ruralhotelsmallorca.com/?gclid=CNzMivnRztUCFXUz0wod99wH_g
Speak with the friendly and helpful Henrick and book a few nights at the quite stunning Cas Sant, a gorgeous old Finca that has been in the same family for 300 years. Arrive, walk 8 minutes to Calle de la Luna and hire bikes from Tramuntana Tours: http://www.tramuntanatours.com/
We hired a couple of Trek Emonda SL6 Pros from them. Good climbers and descenders, which is most of what you do in Mallorca.
If you don’t fancy a lovely old finca, stay in Port Soller, which is a nice quiet lttle resort and not full of package towerists then hire the bikes from Tramuntana’s other shop on the front. From Port Soller you can climb directly into the Tramuntana mountains or take the boat to Sa Calobra for the amazing climb over the mountains and back round to Soller.
Only one caveat: don’t get shafted with extra charges at the car hire desk like we did.