After being there without my bike, I can only envy you. It looks frickin’ immense as far as biking possibilities goes. Google for mountain bike clubs in Jakarta, and start from there. If the MTB clubs are anything like the Hashing clubs, you’ll have a great time. Loads of ex-pats, loads of locals, loads of good food and beer. I think there may be some MTB-Hash clubs as well.
For accomodation, try airbnb.com. Places to stay in all price ranges and all locations.
Temperature-wise, when it gets hot over there *NOTHING* will keep you cool on your bike. You need to get out of the sun when it’s like that.
If you want a real wilderness biking adventure, head over to Flores Island (Nusa Tengurra Timor) and bike from Labuan Bajo to Maumere. We drove it, but the roads and scenery were absolutely breathtaking. It would probably take a week or so, and definitely requires a guide.