I'd also go with the guide gun, but I'd carry the Sig 229 .357 Sig on my hip. If you are really going to be attacked then a rifle can be tough to get in action quickly and is no good if you get knocked down and that beast is on top of you. From underneath you've got a good shot at the throat or the lungs.
Making your presence known in order to avoid the tragedy entirely is definately best. Well armed you might come out the victor, but a dead grizzly is no victory for the American wilderness.
You never know though. I heard a story recently involving a rogue grizzly that was absolutely HUGE. The guy was in a situation where he had to defend himself and he just stood his ground and opened fire with everything he had from a handgun. (not sure what cal) He put 34 rounds into it before it finally laid down. When they took a look into the grizzly it had remains from two humans in it's belly.
what about accuracy with such a short barrel? it would make a sweet carry gun in a nice horizontal shoulder holster!
I personally find that I shoot revolvers very accurately if ya cock the hammer. I've shot a 357 w/ that size barrel before and did fine. I would think at 7 yards or less, U'd be fine.
The Alaskan retails for $899 so actual dealer price is probably on target with your budget and your purpose is exactly what the gun is designed for. I'd go .454. I suggested the rifle primarily because I hate to see anyone buy a gun that is so singular in purpose the it doesn't get use. At least a rifle is perfectly good for hunting when you aren't on the the bear defensive, but hey it's your money and heck that Alaskan looks like a damn fine gun.
Read an article where someone killed a bear with a Glock in 40 S&W. In Minnesota, one can hunt big game with a 357, 10MM, 41mag, 44 mag or any 50. I have an EAA Witness 10MM (Wonder finish) that I use for hunting. They run around $400 or less. The factory 10rd mags can be easily altered to hold 14+1. I have had no problems with the gun. Good accuracy, easy to carry, and pretty inexpensive. Then, one COULD use it as a carry weapon, should they choose.