First, it’s irrelevant that I have to change my CG to tilt the bike. What’s relevant is that it is very easy to do so. The fact that it is so easy to do means that gyroscopic precession is not going to help you stay upright.
I have no idea what you mean here. “The bike is not tilted at all”? That is observably wrong. Again, the fact that I am able to easily tilt the bike means that the bike tire’s gyroscopic precession won’t have nearly enough force to keep someone upright.
For those really interested, here is a good source. The third edition. Earlier editions were inferior WRT the stability and steering chapter.
It is not the force acting directly, but gyroscopic precession DOES produce a steering torque on the front wheel that tends to steer the bicycle back towards a balanced state. Also it is a primary factor in being able to ride and steer a bicycle no handed. Jones rigged up a counter-rotating wheel that canceled the gyroscopic precession and showed that it is NOT a primary factor in normal (hands on the bars) stability.
One huge factor is due to the trail and angle of the head tube. This produces a turn toward any lean, and also creates pro-stability steering torque if the lean angle is incorrect for the turn. If you hold a bike upright and push the front to one side (without tipping the bike) the front wheel will steer in the direction you push. Centrifugal force (I know, I know) mimics this action if the turn is not coordinated, turning the wheel toward the center when skidding and toward the outside if slipping (airplane terms).
Ok, what I meant was you can change the orientation of the bike to the road, but you still end up with everything balanced on either side of the CG.
And you’re right that gyroscopic precession isn’t enough to get the bike realigned, I didn’t pick up that you were referring to that. It allows the bike to ‘track’ straight, increasing the stability and minimizing your input.