Regarding non resident - from State of AK regs:
A nonresident who hunts brown/grizzly bear, Dall sheep, or mountain goat must be personally accompanied by a licensed guide OR by an Alaska resident over 19 years of age who is within the "second degree of kindred"
That means unless you have family here that will go with you, it is going to cost you.
If you have family, it can be done for less, but just getting to where you are going to start hunting ain't cheap. Figure $1500-$2000 for airfare from L48 to rural hub community, and then getting from rural hub to hunt will be another $2k-$3k per head (ish)for a fly out. Add to that the gear that you will probably have to buy that you don't already have, and things start to stack quickly.
If you really want to hunt bear, moose, or caribou 'on the cheap' may I interest you in a career in health care? Lots of health care jobs available if you are willing to live, work and play out here. Check out www.ykhc.org
(Bethel based healthcare organization) or www.bbahc.org
(Dillingham based healthcare organization) and spend a couple years in the bush!