Not seeing the correct answer here. Though the gyroscopic effect helps a little, it’s minor. If you ever did the experiment in school where the teacher had you hold a spinning bicycle wheel on a handle, you know the effect is there, but you also know it doesn’t take all your body weight to overcome it.

The real answer is steering: on a moving bike, if you start to lean one direction, you can just turn the handlebars slightly to turn into it. That’s why on a bike moving slowly, you find yourself steering back and forth like crazy to maintain balance, but on a fast moving bike it seems almost effortless. Also, the way bikes are designed, they’re somewhat self-correcting: if you lean over on a moving bike, the wheel turns to that direction.

On a treadmill, both the gyroscopic effect and the ability to steer into the fall should be in place, so I think it should be stable.