If a rocket had gyroscopes big enough to do that it would never get off the ground. They use small gyroscopes to control servos that move the rocket engines enought ot control direction. The gyros only dectect change of direction, in other words they act as an autopilot.

In fact be glad that the gyroscopic force involved on a bicycle wheel is small, because if it was large you would not be able to control the bicycle.

Bicycles are dynamically stable, a criterian bicycle slightly so, a roadster very much so, but they are statically unstable. Which is why it is so hard to balance a unmoving bicycle, you have to do all the work with body movement; and so easy to balance a moving one, you only have to correct for perturbations. In fact if you had a perfectly smooth level road with no wind your bicycle would follow a straight line without a rider until it slowed down to the point where it would fall over.