You have a rifle for one and you will never be fast enough, if Porky, Yogi or Cindy come for you. Any and all of 'em will be on you before you'll know it.
As much as I'd like to fight for my rights to carry a handgun in the bush, a shotgun is more effective
Some what of an aside, but the prevalent scenario people envision is our beleaguered hero stopping the charging nasty critter with a well placed shot or two. And certainly, a long arm is much easier to shoot accurately and generally can be expected to have a lot more stopping power.
The 2000 lb elephant in the kitchen that nobody thinks about (or wants to talk about) is that a lot of people find themselves needing a bear wrench AFTER they find themselves on the ground being gnawed on. What are your plans for getting your long gun into action in THAT situation, with it underneath you, only one hand free, etc? A handgun is short enough and intended for one handed use that you can get it out of a holster, and start putting holes in fur at contact distances with one hand while your other arm is being chewed on, busy trying to defend yourself, etc. A couple of years ago, just across the border south of here, a Montana hunter shot a cougar off his back with a handgun when it had him down on his stomach and was trying to chew its way through his backpack to his neck. I can't imagine I would ever have my rifle AND a handgun while out elk hunting as he was, but he certainly wasn't in a position to bring his big game rifle into the effort. Stories of people carrying handguns who used them to resolve the issue while down and fighting for their life with a critter are not unusual. Yes, there is also bear spray, but spraying a bear's ass while the biting end is working on your legs is probably not going to be that effective at getting their attention.
Somebody might ask the officer who advised "just get a shotgun" how he personally would deal with that issue.
I have an ATC and have had one for quite a while for my sideline business. Based only on my own experiences, if you fit the magic criteria of "works in the bush" and explain why carrying a "more effective long gun" (see above) won't suit your work conditions, it is pretty routine after that. In fact, they waived their requirement that I present myself to a local club's range officer or an RCMP officer to desplay and get signed off on my competence when I sent them CF bumpf indicating I was small arms instructor and urban ops instructor qualified. Given that the range officer in question could have been nothing but a diehard skeet shooter or the member one who just barely passes their annual qualification, that might have been a very interesting session indeed. I would like to see how they did it! Similar to a CF austere range shoot, perhaps? Teddy bear mounted on a post a dozen feet away?
Relevant to the situation at hand, by all means mount a legal challenge if you want. No point declaring defeat before you ever start. But I think the chances that the Canadian government bureaucracy (i.e. the people who REALLY decide issues like this, not the government of the day) will relent are exactly zero. Similarly, I don't think it is sufficient an issue that the elected critters in Ottawa will get involved and order them to change their policies. If hikers and fishermen were being killed by the dozen, perhaps, but that isn't happening enough to justify the "risk".
After all, we all know that somebody might put out an eye if defensive handgun carry in backcountry areas were allowed.