If you want to spend time mountain biking, I think that rural Kyushu or Shikoku, would suit you better than Kyoto. You can stay at a deluxe ryokan. The coast of the Seto inland sea tends to be warmer than most of mainland Japan, as does the south of Kyushu.

Another option to consider - not far from Tokyo - would be the Izu peninsula. There you can find warmer micro-climates, luxurious ryokan, and some interesting country to explore. I'm pretty sure there must be some good bike trails around there.

The Outdoor Japan site has some articles about mountain biking in Japan
http://www.outdoorjapan.com/