I had been living in Tenerife for two and a half years until March of last year and it is very mountainous as soon as you leave the coast and there are very few places to cycle unless you like climbing. There is some fantastic mountain biking available and if you need any further info. regarding this please let me know. At least in October it will be cooler but hopefully still nice and warm.
We are also hopefully going to visit for two weeks in October to see our friends there as we have not been back since we left last year.