You should think about a little more stopping power like .375 or bigger. You can get it done with a 7mm but if he's coming down on you your going to want enough energy to bust him down and keep him down.
Myself I would hunt with the 7mm if its all I had but I would make sure my buddy has something a little bigger if needed.
My opinion. If you can drive tacks with it, use what you got. Just be sure the bear has no idea whats coming.
I agree with Bear74. I love my 7mm Rem Mag but it is not the best for big brown bears. Blacks, yes. If you are going to use it, get the heaviest premium bullets your rifle will shoot well, 175 grain Barnes maybe. If you have access to one, I would consider a .338 or .375.
I know a guide that shoots a 7mm for hunts on Kodiak. I was pretty surprised by his choice in calibers but hey... its his job, not mine. At any rate, he makes it work. For me, I wouldn't hunt with less than a .338.