30 cal bullet for Brown Bear

If your gun shoots the 180’s accurate, I wouldn’t worry about the 200’s.
If you have a 375 and can shoot it well with 235’s or 260’s I would recommend that. I person used the .375 on my Grizzly.
I definitely would feel comfortable with the 300 mag though.
The 180 or the 200 PT or AB would work just fine.

You're on a guided hunt. Shoot straight on the first shot and let your guide worry about the rest. Most guides worry more about clients who can't shoot than if they're shooting a big enough gun. A solid hit with a 300WM using a good bullet is going to make the rest of it a lot less trouble.
Guides do get a little jumpy when folks show up with heavy hitters. So many just don’t shoot them well. Dad killed six up around Ft Wainwright with an 06; one with a 12ga; one with his sheep rifle, a .264wm. Said he shouldn’t have started the fight using a 264.
Who are you hunting with?