Hi,Belive it or not, I carry my MP with my on almost all of my bike rides except the races and long/hard-core road/off road rides. I ride primarily cyclocross and road but occasionally hard-core off-road (mtb). In any event, I almost always cary the camera in my messenger bag. I use the old school timbuk2 pee-wee bag. And I must say that the camera is much more accessible to me from the shoulder/messenger bag.
However, if you don't do nay aggressive and fast riding, you'll be fine with a frame/handlebar mounted bag. Except I still think that a backpack or a shoulder bag is better since your body will absorb a lot of small shocks that the bike frame would not.