I used to use a bike a lot to access non -motorized areas for elk/ deer hunting. I showed up at someones back country horse camp on my bike one day and they couldn't believe their eyes.
Also, me and a buddy ended up packing a bear out on a bike once. Quite a sight, draped the head and front legs over the handle bars tied it down and pushed it out.
You can cover a lot of ground quick on a bike. I really like the idea. It would be great way to get back to your truck when ditch hunting; just drop it off at the end of the cover, drive to the other end, hunt the ditch and ride back to the truck. Save a lot of time and leg wear.
No problem carrying a gun, just get a shotgun sling.