One thing that hasn't been mentioned is tyre grip on the Moon.
It works out that at 1/6 of Eath's gravity (which is what you have on the Moon) the rubber tyre grip goes down to 1/4 of what it would be here on Earth. (not 1/6, because the coefficient of
friction goes up by a factor of about 1.43 for a 1/6 load)
So if a bike on Earth can corner at 1G (9.81m/s/s), on the moon the same bike has max cornering grip of only 1/4G.
So in that sense it would be harder to stay on it. - You'd have to corner a lot slower to keep the bike from falling away from underneath you anyway.
Oh, and braking. You wouldn't be able to stop as quickly for the same reason. Or accelerate - bikes accelerate pretty fast from a standstill here on Earth, so just getting going could be quite difficult - though I admit I've never tried this myself..