I did a very cheap and cheerful "static home" (pretty much like a caravan on a camp site) in the late 80's, but we did hire tandem, It may have been single speed or a 3 speed SA hub, and cycled over to Formentor & back one day. 60km round trip. Does that count?
Can Picafort was pleasant enough, typical Mallorcan beach town. Puerta Pollensa is a bit nearer the mountains if that's your thing and will have more choice of bike hire places, I guess Can P gives you more options for non mountain stuff.
There is a thread somewhere worth looking at - maybe touring section, a chap used a few trains to places and then cycled back on Mallorca. there is a line from Sa Pobla into Palma.