Hi Michael. I used to stay further west at Los Cristanos. A couple of our rides were upto to Vilaflor then onto the top of Teide. On our rest day we would cycle to El Medano just a little east of where you are staying -nice coastal town with plenty of cafes.
There are a few routes upto Vilafor from your hotel one thru Granadilla, we would join from west side but you would attack more from the South.
Here are a couple of screenshots of suggestions, first one is upto the viewing point on the edge Caldera, great view of Teide . Second is if feeling adventurous and want a loop, which was similar to a route we used to do in reverse.
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There are cafes at Vilaflor (popular stopping point) half way up and pretty much your last opportunity to replenish before going onto the top.
Expect at least a couple of hours to Vilaflor and another hour to the top viewing point. Expect 6-8hours if wanted to do the whole loop.
This third route is a lumpy up and down to a town called Guimar slightly inland further east , again this was our queen's day to Guimar upto to the top of Teide over the top and back down. Between 90-108 miles depending on start point over 10000ft of climbing and at least 8 hours
I can provide gpx file if you want, but this gives you options
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