+1 for Andy at Tramuntana Tours.
Not sure what bikes he currently has to rent, but you’ll probably pay around €20 per day max and can set the brakes up as you liki.
The riding is like Southern Spain, dry, rocky, warm. Plus the beach is always close by. There’s a German guide book I think and a few websites with routes, but ask Andy for advice. Much of Mallorca is privately owned and the owners can be viscious I hear (though never had a problem personally). My favourites were the Lighthouse ride, Barranc route and the GR footpath to Deia from Soller.
You might not see another mountain biker but will see plenty of roadies.