To keep upright and achieve balance when moving, you steer the bike so that the effective centre of gravity is always over the point where the tyres touch the ground. If you start to fall to the right, you steer to the right, and centrufugal force on you and the bike acts to bring the bike upright again. The faster you're moving, the greater this centrifugal force, and the smaller the steering movement that's needed. But when moving very slowly, or stationary, you still have to keep the centre of gravity over the tyre/ground contact point. Then, there's none of that centrifugal force to help you and you have to depend on body movement alone to stay upright.
The centrifugal force of the spinning wheels actually has little effect. If it did, the vector forces of the wheel versus the direction of the Eath's spin would make it harder to steer in one direction than the other. (Ask anyone who has lifted and carried an operating gyrocompass. it'll turn easily with you in one direction, but almost knock you over if you try and turn it the other way!)