In 73 Uncle Sam sent me on a "trip" to Alaska for 3 years. Upon arrival we all had to go through an indoctrination course that lasted 3 or 4 days. The last day was out in the field.
They told us that if we wanted to fish or hike a "large bore handgun" should be a with us at all time. They also stated that the 357 mag was not considered "large bore".
I know this information is over 30 years old, but I will put it out there and you can take it or leave it.
First I wouldn't buy a 30-30 for brown bear, but if it is all I had, I would work of bullet placement.
Most of the hunters up there (then) preferred some sort of manual action. Why? In case some snow or water froze the action you could "force" the action to get a 2nd round up.
If you fired your M16 at 20 below or colder, if you didn't at least wipe the bolt down, it would freeze. I've seen 105 recoil mech. ruptured because of the cold. And that was after they put the winter weight oil in it.
I had my Marlin 30-30 up there, and it took a Moose. I also saw a 357 mag take a moose, barely. (I should note that I didn't take the moose, I loaned my rifle to a friend that didn't have one. I was using a Rem. 700 30-06 lefty.) I only mention it because just about ANY round can kill, if everything is JUST RIGHT. I wouldn't buy either if I was going to be in brown bear country. But if that was all I had, and it was the difference between being mauled. They would find a empty gun beside my remains if it didn't work. If it did work I would have a great story, right after I cleaned my pants.