A guide would be required for a nonresident hunting grizzly bear or sheep in Alaska. I can't speak for what your guide may or may not allow with respect to long rang shooting. I think others have already given you some good advice there. I've hunted all three of these game animals for the past 30 years, and from numerous first-hand experiences, I can say that sheep and moose are relatively easy animals to dispatch at either close or long range. But grizzlies, coastal brown bears, or even black bears need to be hit very well on the first shot.
A moose offers a huge kill zone, making it a pretty simple task to hit the lungs at longer ranges. A lung-shot moose won't go very far with any expanding bullet that penetrates far enough to get through both lungs. Dall sheep are relatively frail animals. They are disabled and die under less physical trauma than other similar sized animals I've seen harvested, such as goat and bear. Sheep hunting can present very long shots. You'll not only need to know your cartridge's ballistics on level shots, but also on angled slopes up to 50 degrees if you intend to shoot at any distance. There's a big difference in bullet trajectory over long, sloped distances compared to shooting on the level. You will spot sheep a long ways away (as will they you if given the opportunity). I've killed dall rams from 13 yds to over 750 yds. I hasten to even mention this for fear of being piled-on by those quick to impose their ethics; should you happen to hit a sheep less than perfectly with a first shot, the terrain is often wide open and based on their nature, you'll generally be afforded additional standing shots. With any kind of decent hit, they won't be able to muster an up-the-mountain escape. You'll usually have opportunity for additional shots to ensure a wounded animal isn't lost. But as mentioned by another poster above, you have to consider the setting and the animal's ability to quickly reach cover, cliffs, or terrain which could prevent recovery of the animal.
Bears are in a different category. They die easily enough with a good hit through the lungs, but the difference with bears is you better hit them pretty darn good on your first shot. Bears usually get up and go at the first hit without offering a lot of second chances for standing still follow-up shots. Once they've been hit, they won't run a short distance and then turn around to figure things out. They generally keep going until they reach cover or disappear over the mountain, if in mountainous terrain. Nothing harder to recover than marginally hit bears. I shot one high in the lungs on Kodiak Island last month. Tracked him for about 400 yards across completely white covered mountainside. I never found even a red speck of blood against that completely white background - I mean not one drop of blood. Fortunately, the bear was hit hard enough that he bedded down out on the open mountainside about 1/3 mile from where he was initially hit, and we were able to finish him off. I'm really hesitant to shoot bears at longer ranges, due to the difficulty in recovering marginally hit bears. Plus they bite back if given the reason and opportunity.
I believe your '06 is up to the job for these three animals - provided by bear we mean black bear or inland grizzly. For large coastal brown bears, I believe you'd be better served with a 338. Yes, you'll kill them with an '06, but a 338 RUM class cartridge will hit them with notably more authority, which is never a bad thing.
Thought you might find my experiences of interest. Enjoy your hunt. As has been mentioned, do what you can to help ensure you get a competent and compatible guide.
