Hello Mark
We have always hired bycycles whilst on holiday in PP. I think that there are at least half a dozen places that do it.
One very good place is on Calle Juan XX111 (the main road from Pollensa) on the opposite side of the road from the Syp/Eroski supermarket.They have a good selection to choose from and you can hire for half a day to a week.Also they have very reasonable rates.
The cheapest place that we have found is a small shop on Calle Bot (the road to the sea,next to the Hotel Pollensa Park) Not a great choice of bikes but it is run by a very friendly Spaniard who is very helpful.
Also in this area the Panorama Hotel have a small selection of machines for hire (just behind the Golden Lion)
Multi-Hire on Mendez Nunes is another choice nearer to the centre of town and there is also a very posh shop around by Los Zarzales which will even deliver the machines to your apartment or hotel.I cannot for the life of me remember the name of it but as you can imagine it is not cheap.
Hope this has been of some use to you and that you do hire bycycles.Its a much better way to see PP rather than just sitting in a car.Try the small road out of the back of LLenaire to Pollensa,a very nice ride indeed.
Cheers