I totally agree with Mart. I have killed a griz with a .54, but a percussion and conicals. The guide is the one that is taking a huge risk in allowing a flinter and round balls, and if he is confident, there is no reason not to try it. If he is backing you up with a .375, you will be fine. However, one thing I have learned from living in Alaska for the last 23 years; if it can go wrong, it will. The climate, terrain, weather, etc., can be brutal on you and your equipment. Make SURE your flinter is in excellent shape and can take some abuse. Have you had much experience in hunting in a steady downpour that can last days at a time? If not, this is something for you to prepare for, as this possibility always exists, especially if you will be hunting near the coast. One thing most of us do up here is tape the muzzle. Yes, I said tape the muzzle. put a strip of electrical tape across the muzzle every day, and this will keep moisture, debris, mud, dirt, etc., out of the barrel. This is especially critical if you trip or fall and jam the muzzle in the ground. Happens to all of us at one time or other, and a muzzleloader is more difficult to clear that a bolt action. The air pressure ahead of the bullet blows the tape away long before the bullet gets to the muzzle, and it creates zero pressure problems. It works, and may save your hunt.
Black powder is available readily in Anchorage, as Mart said. If your guide is a good one, you can arrange for him to have a can for you when you arrive, or take you to purchase it. He should know where to get it, even if you are going to a remote town. I agree with the analogy of carrying a .454. If you are not comfortable carrying one, and have never shot one of that magnatude, you will only create problems for yourself if you do carry one "cold-turkey". I have carried either a .44 Magnum or a .454 with me on nearly every excursion I take for the last 23 years, and I still don't like the extra weight. But, I am used to it and am very familiar with the weight and recoil of these weapons. Let your guide deal with that, because he will be with you 24/7, or had better be.
Good luck, and have fun!! One thing I HIGHLY recommend, even at this late date, is to get in the best shape of your life. If you are just in "urban" shape, you will be defeated at the onset in Alaska. The terrain here in most bear areas can be brutal, and if your legs can't get you double-time up the mountain or across a willow and alder tangle to intercept a bear, you will have a small chance of success. Most guys that come up here thinking they are in good shape for life in suburbia are quickly humbled. Again, good luck and enjoy yourself!!!! I live here and bear hunt regularly, and the thrill is still there every time I go, which is as much as I can get out and go. I am going on a hunt in the interior in a couple of weeks, and I am getting antsy even now with anticipation. Our snow is FINALLY melting, and bears are coming out!!!!!! :applause: