Just a thought I had today while biking home from work and I don’t know enough physics to answer it
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Lots of effects working together for that to happen, I’m going to explain one but it is not the only factor.
Angular (or rotational) momentum. Basically, since all of the mass in a bike wheel is at the edge, when it spins there is a lot of force and momentum along that edge (due to the mass spinning in a circle quickly). This causes the wheel to want to stay on that axis and resist any attempts to deviate.
I had a physics prof in college who brought in a bike wheel with handles at the axle. He’d have someone hold the handles, then spin the wheel and tell them to try to tilt it. It is much harder to turn while spinning. If you have an old fidget spinner, you can test it yourself by trying to rotate your hand while it’s spinning vs not spinning. This is also the core concept behind tops and gyroscopes.
So when you are riding your bike and you have some speed built up, your tires have a lot of angular momentum and they will resist the forces that would normally cause them to fall over. This effect works in synergy with other effects people have mentioned here and you are able to keep your bike upright.
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