We’re going in September for a “normal” holiday but I’m planning on taking the mtb. I’ve found a few routes using strava and OpenStreetMap, from Las Lajas doooooown the hill towards Adeje. You can download other people’s routes from strava if you are a premium member, so woohoo for their free trial month.
The strava heatmap is quite useful for working out where other people have been too.
A ST article from a while back (issue 77, IIRC?) covered Tenerife; they mentioned the National Park bus that will take bikes up towards the edge of the National Park so you can bike back down again without having to finish where you started.