You aren't allowed to drive a car on a public bridleway for a start. I wouldn't have thought it was legal because it's a public right of way and that could lead to all sorts of problems, but I'm sure there will be people on here that can tell you for sure.
What kind of gun? Was it a shotgun, as in, was he trying to shoot game, or a handgun?! I would report him to the police for driving on a bridlepath and tell them that he has been using the gun whilst on there.
i rang the police as he was v agressive when i queried him being there, and they basically werent bothered as the farm the public bridle way runs through is private land, i have always thought public actually meant that
it was a shotgun and he was supposedly shooting magpies, although i could see none, and the field he was shooting into has horses and cows/calves in it