I don't know for certain, but I can't use a treadmill without holding on for dear life; yet I can walk fast and even jog for a 5k. I think it is Newton's law "a body in motion stays in motion". I think this would work for a bike, but getting started and stopping would be the hard parts. It takes me back to teaching my kids - I would start them and stop them. I think a bike without the cross bar (old fashioned girls bike) would help on the stop.
Good luck, your success would be a triumph and an inspiration for all of us.