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@lae
With regards to centrifugal forces - gyroscopic forces don't have any effect on the stability of a bicycle. Gyroscopes only work by constantly changing heading relative to their 'axle' as it were - but bicycle wheels rotate around a fixed axle.
Bicycles remain upright through the same mechanism that allows you to balance a broomstick on your finger - by moving the support directly underneath the mass. With a broomstick, you move the support (your finger) whilst the mass (broom head) remains pretty stationary. On a bike, the support (the point where the tyres touch the ground) stays in the same place, but the mass moves around relative to it.
Both of these points are evidenced by the fact that if you lock a bike's steering, it falls over even if it's moving.