Like any reasonable caliber, it will work if used properly.
Two of my friends who guide for bear in Maine both have complained about 270's, however, having tracked a few bears that seemed to have been hit fairly well with that caliber. They recommend the heaviest bullet available if their hunters insist on .270.
From personal experience having killed a few bears with a few different calibers, I really like the 30.06.
That said, I've killed them with arrows, too. I think bears are a bit different than other game animals. You might encounter an average 150 pound bear which isn't much harder to kill than a whitetail, or you could very well run into a 400 pound monster (PA has some big bears). I'd rather be overgunned for a small bear, than under-gunned for a brute.
Best of luck to you. Bear hunting is some serious, heart-pounding fun.