Inland Grizzly or coastal brown bear? Inland grizzly would be less expensive, but not sure how much. They aren't much bigger than black bear either so most anything you'd feel comfortable with for black bear would work.
I asked a guide who posts on another forum a while back just out of curiosity. He told me $20,000-$40,000 depending on the outfitter for brown bear. That doesn't include transportation there and back or taxidermy.
I know that my taxidermist checked into it and found it a lot cheaper to fly to Russia and hunt there rather than Alaska. We didn't discuss price, but he said it was 1st class.