Loads of routes, we stayed in Costa Teguise about 23 years ago and just got on the bikes. I went with a mate and ended up proposing to my now wife when I got home - he wasn't up for beers at night and it was a bit quiet. this was before Garmin days - just get a map. Check out the Lagoons at the top end of the Island that are pink and green, then you've got to ride up and down Fire Mountain. It's fast and you will overtake cars. It is windy as hell there and there is no let up.
I wouldn't get too stressed about routes as it's not that big - you can do a lap of the island before lunch. Drivers are a revelation compared to the UK