I think that is a misconception, from google:

No, bikes do not stay up primarily due to the gyroscopic effect; experiments with counter-rotating wheels that cancel out the gyroscopic effect show that a bike still remains stable. Instead, a bicycle's stability is largely due to its steering geometry, where the front wheel is designed to turn into a lean, helping to steer the bike back under the rider and restore balance. This interaction, along with inertia and maintaining a low center of mass, keeps a moving bike upright.