It has never occurred to me to carry a gun while cycling. I've never felt unsafe on any of my rides. The worst thing that's happened so far, was on one occasion being chased by a not so nice Pitt bull. And on another ride alone on a trail I encountered a deer on the side of the trail. I carry a whistle, so I stopped and used it thinking it would scare the deer, but the deer had other ideas and started trotting towards me. Obviously I turned around and started pedaling and the deer trotted behind me (just like a dog..lol) for acouple Km's. I ended up having to take the long way home that day!.
Seriously I can't imagine living in a area that I'm so concerned and afraid for my well being that carrying a gun would be the solution, never mind a loaded gun. Maybe you need to move?