It works on its own. If you push your bike along with a good run and then let go, it’ll stay upright until it slows down too much.
Learning to ride a bike is mostly about being confident enough to let the bike work itself out. It gets more stable as it goes faster, but it’s natural to be afraid to go faster when it already feels unstable at low speed. Then there’s a little bit to learn about countersteering, but most people figure that out without being told it’s even a thing.
Yeah. Case in point: Ghost riders in Motorcycle racing.
Motorcycles also tend to fall down when stationary, yet stay upright without the rider at speed.
Also makes me wonder if just the bike crossing the finish line would be enough to win if you fell off in first place just before the line.