It's a lot more difficult to hire a motorbike in Tenerife than a car. Presumably because riders are a lot more likely to crash than drivers. Remember that none of the secondary roads in Tenerife are straight, so take care, and make sure you take out insurance to cover yourself in the event of a bike accident. Also, watch out for hunting dogs up in Las Cañadas on Sundays & Thursdays.
Here are a few links to motorbike rentals in Tenerife:
www.motoslasvegas.com (Puerto de la Cruz)
www.canarYmoto.de - seems to have the best bikes, like for example their pristine Kawasaki Z750 & Z1000s...
www.rentamototenerife.es
www.expo-motor.com (Los Realejos, Tenerife)
www.motocross365.com (Arona, Tenerife)
www.teneriffa-on-bike.de
www.mototours.de (based on the island of La Palma)
www.motostivolirent.net (based on the island of Gran Canaria)
http://www.canary-island.com/gc/00_spa/ ... n-fun.html (based on the island of Gran Canaria)
www.bikecenter-gomera.com (based on the island of La Gomera)
Quad bike rentals:
www.xtremerentalstenerife.com