As much as I'd like to, I can't imagine actally being able to shoot from my moving bike. It seems too much risk as the road is more likely to kill you than an on road gunfight. I do however carry often while riding. When riding, I prefer a very stable holster and a thumbreak.
There is fair argument for not carrying on your person while riding as a large hunk of metal on your person may not be a good thing if you have the misfortune of sliding down the pavement with your gun on the downside, and probably other concerns that I don't know of. I wouldn't like to have my gun be separated from me during some sort of accident either. A gun seems to be the least useful tool for survival on a bike, but I'd rather be prepared for that freak circumstance, while I focus more of my interest on safe riding.