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.
Newtons first law of motion: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus illud a viribus impressis cogitur statum suum mutare.
A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by a force.
So, when you’re on your bike and you’re both in motion, unless other forces interact with you, the momentum you have will keep you upright in a straight line.
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