I went for a holiday at the end of June (not biking related, really) but I did manage to sneak a ride out.
I stayed between Playa de las Americas and Los Cristianos and hired a bike from Bikepoint in Playa de las Americas.
They had a decent range and were very helpful. I hired their cheapest bike which was alloy framed with full 105. I think it was a Ridley, but they had a wide range with everything up to full carbon with Di2 & discs.
I also hired a helmet and mtb spds.
They were helpful with routes and there looked to be lots of rides from the area.
You will be going uphill a lot!
I did a 30 mile ride (15 mile up & then turned round & came back down). In the 15 miles up, I did around 1400m of climbing.
Take decent suncream – it was bloody hot with no shade.
EDIT – here was my post asking for advice:
http://singletrackworld.com/forum/topic/cheeky-days-cycling-in-tenerife-anyone-done-it