I would never, ever, under any circumstances try to engage my gun while riding. My first thought is being able to control the bike; maneuver and evade.
If you think you can shoot while underway, more power to you. But I think it's not an option.
As you said, you need your hands on the controls. But then what happens if you have your gun in hand, and need to put your hand back on the control? Are you going to drop your gun? Tuck in under your leg in time to get your hand back where it should never have left- the control?
Entirely unrealistic to think you can deploy your gun while riding, in my considered opinion. I'm more concerned about when I'm parked or off the bike.