It's hard to mix riding and shooting, especially when you're covering any kind of distance. To shoot, you have to stop, unpack everything while you're still sweaty as hell because the wind has stopped, take whatever pictures you wanted to, pack everything back in, start up again, etc. I found that I just left the camera in the bag for most of the ride since I didn't feel like going to all the trouble.
Oh, and riding during ideal light for photos can be a bad idea if you're riding into the sun, unless you don't like being able to see what's on the trail ahead of you.
I'm planning on going to Utah this summer or fall, but I probably won't bring my MTB since it's not setup very well right now and I don't feel like replacing a lot of parts. I mostly ride BMX now.
Hiking is a lot more conducive to shooting, and you can use a monopod as a hiking stick if you want 😛