I visited Tenerife last summer for a holiday and enjoyed 3 excellent days mountain biking. It was a nice compromise as the wife likes to sunbathe, but I don't so I organised 3 days guided riding over the fortnight. If anyone is going to Tenerife with the other half or the family it is well worth trying to sneak a day (or 3!) out on the bike. I arranged eveything through daz at lavatrax and all ran smoothly. I was collected and returned from my hotel and bike hire was included for around 55 euros for a full day. Excellent value and great riding.
I stayed in Los Cristianos, but they will pick you up from anywhere within reason on the south of the island. The tour guide lived in a town called El Madano (think thats how it was spelt) and there was also a mtb shop there.