The gyroscopic effect of the wheels. As the speed increases, the centripetal force of the wheels increases. The plane of this force is vertical, or upright, and as this force increases, the greater the unopposed force required (I.e. not upright force) to unbalance the bike.
This is why bikes will remain upright without a rider, and why if you spin a wheel attached to the end of a string that is offset on the end of the axle of the wheel, it will continue to remain upright.
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