First off, don't get your hopes up about your chance of drawing a moose tag, even with all of your preference points. There are thousands of other guys who have all their points, and very few moose tags are given out in the entire state, let alone to non-residents.

For quality bulls, a healthy moose population, and lack of qrizzly bears and wolves, there are few places in the world as good as the Big Horn mountains for Shiras moose. In fact, I would venture so far as to say there are several bulls running around in the Big Horns that are big enough to easily make the top 5 for largest moose killed in WY. Equally as amazing as the quality of bulls is the number of moose you'll see. Every time I head up the mountain to do nothing but look for moose, I see probably 30 bulls in one night. Everyone else who goes up there to look at moose can tell you the same thing. The best two areas in the Big Horns are areas 1 and 34. I spend a lot more time in area 1 than I do in area 34, but I know they both hold some real whoppers.

As for the time and place to hunt, it's kind of a crap shoot. All summer long the moose seem like they are everywhere, then as soon as hunting season and the rut nears they become ghosts. The big bulls are big for a reason- they head clear back into the wilderness where they are hard to get to, and even harder to pack out. It's hard to tell where exactly they go during this time unless a someone has been following them or they stumble across them while they are scouting. My dad and I scouted over Labor Day weekend when he had his area 1 tag a number of years ago, and we found a bull that honestly had to have been close to 60" wide with huge paddles and a ton of points. It was definately a record book bull. He was nowhere to be found on opening week of bow season, though. If you're lucky, you will run across a bull that has ventured back closer to the roads in search of cows. That's how my dad and I ran across the 51" bull my dad ended up shooting. Going at the opening of the rifle season would probably be your best bet if you're only going to use a gun. If you're going to use a bow, it might be worth going at the beginning of bow season and trying to catch a bull before he heads back into the wilderness. You also might want to go during the last week of bow season then the first week of rifle season. It's really up to you depending on what weapon you want to harvest your moose with. You also might want to keep in mind that if you go later in the season there's a good chance you'll get hit by a snow storm.

If you have any more questions, feel free to ask and I'll try my best to answer them. I am in no way an expert at moose hunting because it is a miracle to have someone you even know draw a permit, so I have only been twice my entire life. But I do know the area fairly well since I spend quite a bit of time up there.