I don't ride backwards, but wondered if it would make a difference, and if it did, what else was involved as well as gyroscopic forces.
After a bit of searching though, if seems that if you either exchange the wheels for iceskates, or add a pair of contra-rotating wheels to negate gyroscopic forces, a moving riderless bike will still balance...
Either way, I am fairly sure that the dynamics of a bike with a rider are very different.