Drive or draw. Choose.
It's like none of you watch Sons of Anarchy.
Drawing while riding good in movies. Roll on the Throttle. I carry inside my riding jacket. It's more likely I'll have to dump my bike vs. drawing on someone while riding, so I place my gun in a location that will cause the least amount of damage to me if I have to take a fall.
This is the jacket I wear. It's mesh so in the summer it breaths, at speed even on very hot days it is comfortable. It also comes with two winter inserts. I ridden in 40 degree weather with the inserts.
I need a jacket like that and a helmet to carry around when I wear it. The chicks will think I have a bada** motorbike and thus adore me.