Shootbrownelk is correct. Grizzlies withing a 100 mile radius of the park are a real problem. The average adult grizzly is about 400-425, but keep in mind that is an average of adults, sows and boars. The big bores I see usually go a bit larger, maybe 550. However it's the sows that are usually the aggressive ones. Not always, but probably 3 times out of 4.
I will be up there in 3 days. I am going as the "extra guy" with 2 other friends of mine to help pack meat and carry an extra rifle. I will have my Mauser 375H&H and my 454 Casull. I have NEVER been into that area without seeing very fresh tracks and I'd bet I see the bears themselves about 75% of the trips I have been into that area. They are NOT rare and scarce.
I personally have never had a problem with a grizzly. I also have never had a fire get out of my wood stove and light up the hearth area of my home. I have never been in a bad car wreck.
I still keep a fire extinguisher handy, and I wear seat belts every time I get in a car.
I am on my 2nd barrel of my 375, and I have over 9,000 rounds through my 454. I shoot them both well.
But with bears, the ability to shoot is second in importance to your situational awareness. Bears can out run horses in 100-150 yards, so no gun is helpful if you let down your guard. You'll never get off a shot if you don't keep your mind on them.
I personally think the best "bear gun" available today is a 458 SOCOM. I don't have one myself, but I have made several of them. 400 grain bullet at 1500 FPS from an AR with the recoil of a trap load in a 12 gauge, and straight line recoil makes for very fast 2nd and 3rd shots. In short, it's a good warm "45-70 load" from a short, light, fast auto that doesn't kick hard enough to slow you down.
If you are hunting elk in an area that has grizzlies, hunt your elk with a bear rifle. You need not buy a special weapon for "defense against bears"
I am a firm believer in powerful handguns. Not to shoot an incoming bear (that's what the rifle or shotgun is for) as much as to use if the bear gets between you and the muzzle of your long arm.
When I was CEO of Cast Performance I had a thick file of reports from various people, agencies and doctors from all over the USA and a few other countries too. I was surprised at how many people had been mauled by bears and cats (and also some kinds of other animals) who had a good rifle with them at the time, but didn't get to use it. It was far more common than I would have guessed before I read the reports.
Many, in fact MOST of the maulings were against people who were armed, and many of them were armed with rifles and shotguns. But those that got mauled nearly always had one thing in common.
They let their guard down.
Bears and cats are FAST. REALLY FAST!
The one thing I love about a handgun is that you have it strapped to you, not just in your hands or over your shoulder.
If you "loose round 1" in the "prize fight for your life" you still may be able to fight "round 2" if you have a hand gun. In some cases maybe not....but at that point what would you have to loose if you tried?
If that happens you are going to the hospital but I have to believe it's better than going to the morgue.