Riding may be nice but you couldn't pay me to go to Bali. I'd be afraid of riding on a damp trail, getting caught, and being imprisoned for 20 years because they say so. Look at the Chapelle Corby investigation and trial. Sorry but those people are savages.
That's probably the most ignorant statement I've read all week.
Unless you're sh*t stirring, in which case it's funny in that "I'm pretending to be ignorant" kinda way.
As for the OP - I was keen to hook up some MTB trips in my time there, but unfortunately had a major crash on a DH course the day before we headed to Bali. Not so bad, because it forced me to spend 2 weeks doing nothing and it's certainly an extremely easy place to relax, and the local people are simply beautiful and certainly make you feel at home.
Before this change of plans I read about Bali Trailblazers and BaliMountainbike.com and they both seemed like they had pretty similar and decent tours of the Batur Crater area, as well as the slopes of the 2500m giant Agung. Both look like really awesome examples of jungle terrain, along with some nice volcanic formations. I know there's several walking trails leading to the top of Agung. I imagined if it was possible to walk up then ride down them all the way to the ocean, it would be one hell of a ride. I daydreamed about moving there, setting up such a trail and holding MTB Enduros and Megavalaches there. I can think of worse places to live.
As advised earlier, do one of the tours, and that should lead you to more MTB folk who can take you to other tracks.
Good luck, and have a great time!
(P.S. Avoid the Kuta-Legian-Seminyak area if you want to avoid tourists. I swear there are more pisshead bogan Aussies in Bintang singlets per square mile in that area than anywhere else on the planet, including Australia.)