Well, as much as I would LOVE to have one myself, I really think you can find something that will make you happier than a titanium 45. For one, the barrel is just too damn short to do the chambering justice. Consider switching to something with at least 4" of barrel, like maybe a S&W Mountian gun in Colt 45, if you can find it and don't hate the company. Or one of Taurus' standard revolvers, don't recall the model name.
Sure, it's heavier, but if you really intend to try to use it against a charging bear, you might ought to discount the first shot, as half your brain will be on the poop in your pants. That second shot will be far easier with a heavier and more balanced pistol. Same for the third and fourth, of course.
Those little snubbies can really snap back, even in 38 Special. A loaded-for-bear 45 would be more than I would care for myself. But load it moderately with some 200g and you have one heckuva slef-defense piece there.
In fact, I'd even go so far as to say, if I were out and about in true bear country, I'd be holding my gun in hand. I wouldn't mind a trusty rifle, but I'd also feel perfectly content swinging a 454 Casull (speaking of Taurus), since the heaviest pistol ain't as heavy as the lightest rifle. And with a 300g bullet going upwards of 1500fps you have some real power on your side.

I think you could safely work up to as much as 10.2 grains of Unique behind Elmer Keith's 260-grain semiwadcutter (Lyman 454424) in that pistol. In a short barrel, it should give you up to perhaps as much as 900 FPS, since it just breaks 1000 in a longer barrel. I suspect recoil WILL be noticeable on the range, but NOT when the bear is trying to bite you! If a bear is coming at you, try to hit it on the end of the nose! A bullet up the nasal passages into the brain is about the only way to stop a bear in its' tracks with any handgun!!

Bon chance!!

After thinking a little more about it, I think I might be comfortable with even a 230g, but I would use a FMJ or other non-expanding bullet. And incidentally, you may not notice the recoil, but the physics are still there. That thing is going to want to sprout wings and fly away from you, so you better know how to control it without thinking, i.e., shoot lots of the same load in practice. Pain you can get around, but Newton is a bit trickier.

I concur with the hard-cast or FMJ bullet. One of the Cast Performance LBT types with the big flat nose are good for such purposes. I use the 265-grain LBT FNGC from Cast Performance in my .454, loaded down to 1550 FPS.

Sorry, but the barrel is just too short IMHO. The design is for defense against humans, not bruins. The lightest, smallest revolver that meets minimum bruin requirements is the 4 and 5/8ths 45 LC Blackhawk. You can get one for $315 or opt for an additional 45 ACP cylinder for $445.

Mine will launch 360 gr LGCs at 1100 fps and the SS action is not a disadvantage with a 2 hand shooting hold. If you want meaningful protection, you need to carry something the weighs at leat 2 pounds and makes 2 times major with a sectional density of at least .250. In a LGC, this makes a big LONG wound channel and won't be so unpleasant that you avoid practicing with it.

A light, hard kicking revolver with a 2 inch bbl is VERY sensitive to your hold and grip and hitting something that you are not already in hand to hand combat with is problematic.