A 12 gauge slug will stop a bear.... But I have to ask, what kind of shotgun are you going to carry on a bike? I'm assuming it will be broken down and my question would then be is your friend going to ask the bear to stand by while you put it together and get it loaded? I suspect there will be a lot of questions at the border and he might as well leave the shotgun at home.
I live in an area where we find bears frequently (black bears...grizzles are further north on the mainland in more wilderness areas where you probably will not go on a bike). I have had two close proximity black bear encounters this year and have just not bothered them and they didn't bother me. This is not unusual.
Cougar sightings are much more rare and usually will not attack a group of men. They will attack children or small men though. If you see one keep well clear. If attacked or stalked fight like hell make yourself look as big as possible and make lots of noise...they will run off.
I don't have any firearms now...I don't need them. The animals don't bother me and I don't bother them. Just read up on how to just not tease them with food and don't annoy them or get near their young.