Hi Steve
There are bike hire shops on just about every street in both Los Cristianos and Playa Las Americas - we tend to stay in and around Los Cristianos, and I know there are two near the main Square (Av Los Playeros) and having had a look in their windows (dribbling on myself) they have F800GS's and the like, but I can't recall seeing smaller machines capable of off-roading or trail riding. Your find of a Versys for that price sounds pretty good, I seem to remember the prices in more touristy areas being much higher than that.
Not sure if it's your bag, but came across these guys:
365 Motocross and even if you're not using them, they might be worthwhile contacting to find out information on the best roads.
I know that if you buy a map of Tenerife, the brown roads on the mountain areas are passable ('off-road' roads).
As for the other islands - the ferry from Cristianos to Gran Caneria leaves twice daily in the peak season, there's a surprising number of people commute between the islands. Details can be found here:
Fred Olsen
Sorry I couldn't be more help than that, it's not something I've done, hence my envy. But I know that the National Park is drivable - and the north side of the island is definitely better than the south for a less touristy and more rugged vibe.
Sorry for my lack of info!
Have a ball though.....and please let me know ride reports etc when you get back!!