Conservation of linear momentum. The bike is already moving in one direction; it needs more energy to fall over while moving than it does to fall over while standing still. If the bike were somehow moving perpendicular to the wheels (say you bunny hopped sideways, maybe?) it would fall over MUCH easier.
As well, the wheels provide much more surface area for the bike to balance on in one direction versus the other, not to mention how its structure balances it with its center of gravity.
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