I would say, despite it not being what you might want to hear: don't carry and ride. At least not on you: perhaps a tank bag or something.
The statistical likelihood of coming off a motorbike are higher than needing a gun. Significantly higher.
People carry a gun in order to improve their chances of avoiding harm in a confrontation, but having one slapped on your person yet that is precisely what will increase chances of severe injury in an "off".
In any case, on a motorbike, the best weapon you have in a road-based confrontation is speed and agility. That has removed me from many a contact with some of the more "me tarzan" road users...
When the right to effective self-defence is denied, that right to self-defence which remains is essentially symbolic.
Freedom: Please enjoy responsibly.
Any idea that relies on murder for its survival in intrinsically weak.