We still don’t really know how bicycles work.

Seems like someone would have figured out a reason by now! My theory: Every force that pushes the bicycle to the left or right causes the front wheel to shift orientation, even if ever so slightly. Because of the momentum of the bike and the frictional force pushing back the front wheel corrects its orientation. Or, more likely, over-corrects in a cyclical manner causing the center of gravity to sway back and forth like a pendulum. The bicycle quickly settles back into a stable state of uprightness.

Solved! No? Ok, your turn.