[paul cotter (OP)]

Is it the gyroscopic effect of the wheels or fine motor control of the rider?

[alancalverd]

Neither. It's primarily the angle of the steering tube. As a bike leans, say to the left, the front wheel turns left and the bike begins to turn. The resulting centrifugal force on the rider opposes the lean. Negative feedback in its simplest form.

At low speeds, the rider needs to make corrective movements, but the machine becomes more stable at higher speeds. A childhood favorite is a "slow bicycle race" - the last person to cover 100 yards without falling off is the winner!

[Halc]

The resulting centrifugal force on the rider opposes the lean

Rider not even needed. A bicycle, riderless, at sufficient speed (about a running pace) will stay up on its own.
Excellent answer BTW. Yes, it's all in the angle of the steering tube, coupled with the curve of the fork, putting the hub off center of the axis of the steering rotation.

[paul cotter (OP)]

Thank you both. It is something I have frequently wondered about, I could have looked it up myself but decided raise the question here, activity has been so low lately.

[Bored chemist]

So, a motorbike should be able to carry on in a straight line indefinitely.
Funny how the people who build robots don't see it that way.

[alancalverd]

A vehicle that carries on in a straight line or other geodesic indefinitely is called a ballistic weapon. Robots need to be a bit more subtle.

In practice you need to add a bit of damping because stability is only optimised at one speed. Below Vopt the bike will fall anyway, and above Vopt it can flutter or Dutch roll so a bit of fine motor control or laterally moving mass becomes important, but the first-order effect is clear, as Halc says.

[Bored chemist]

OK, so the first order effects is that the road is there. Ballistic missiles are seldom provided with roller skates.

And it seems that " a bit of fine motor control or laterally moving mass becomes important".
That's good to know.

It's said that you never forget how to ride a bike.
Apparently, some folk think that's because you  never needed to learn in the first place.

It is of course more complicated than you think