I carry my pistol the same way riding as I do when I'm walking or driving:
Strong side OWS pancake holster.
I'm an ATTGATT rider and wear protective gear (jacket, pants, boots, gloves, full face helmet). If its too hot to wear the gear, its too hot to ride the bike. I wear mesh mostly so its not a problem underway.....sitting at long stop lights in St Louis summer heat sucks the big one though.
My jacket keeps my shirt from being blown up and showing everyone in the world that the guy on the motorcycle has a gun. No need to advertise to some hoodrat out and about that he can run me off the road and collect a piece for his next criminal enterprise.
I carry this way because realistically, how in God's name are you going to employ a pistol accurately while operating a motorcycle? Accurately is the paramount part here....you go blowing rounds off on the freeway or roads and accidently hit another car and injure someone....you're fucked. Flat out. God help you if you shoot at someone, miss them and hit another vehicle, and cause that vehicle to crash into yet another vehicle....
Alot of police departments have policies against firing from a moving vehicle due to the liability involved. Any decent attorney is going to hit you with that in the resulting civil suit. Unless you can show proof that you've trained regularly to draw, shoot and hit targets while riding your motorcycle, doing so leaves you up shit creek....