I've taken a short barreled pump shotgun loaded with slugs into the bush on fishing trips in Ontario. Despite seeing a few bears, I never had reason to shoot and only would in the event the bear was attacking. I've also gone in the bush without a firearm and not felt any less safe. It depends largely on where you are.
For rules and regs on gunownership in Canada go here:
http://www.cfc-ccaf.gc.ca/en/default.asp
If you are in Southern Ontario, for the safety/hunting courses, I know several people who've gone here:
http://www.shooterschoice.com/
In addition to knowing the gun laws, know the hunting regs. In Ontario, there are regulations that apply to the caliber and ammunition you can carry in the bush during certain seasons.
Paul