Tritium is actually a very weak beta emitter, it can't penetrate your clothing for example, assuming it hit the fibers. The problem is it can exchange with hydrogen in other molecules, i.e., those in your tissues which are bathed in water. So, some could get into your DNA, etc., where damage could be done overtime. I had courses in radio chem and prof talked about the importance of strong an emitter was, form, biological activity, etc., relative go the danger. I don't like this either, but the risk is pretty low. The general rule is storage for 7 half lives before releasing material, but storing all this water, and more to come, for what I believe would be 150 yrs, also has risks, like a one time mass release in another quake.
The only real solution for this and other similar hazards is stop making the stuff.

As a final point, we use much hotter isotopes medically daily. I got iodine for a thyroid test, you could see it in my system with a geigor counter, yet I was allowed to walk around and piss it away, etc. If a research animal, all wastes and the animal would be collected stored, burned or buried in time. Years ago, a team checking out nuclear reactors found a hot spot, it was a waste treatment plant radiating due to all the stuff used medically. Many isotopes are made and used in medicine, testing for infections, cancer, etc. some so hot they can set off every instrument even rooms away, the stories say.

That's a difficult decision, and unless she's one hell of a pistol shot, it likely wouldn't do much good anyway.

She'd need either a .44 Magnum, .454 Casull, .460 S&W, or other such caliber in a handgun; a rifle in .300 Win Mag, or larger for a rifle. Second, the bear likely isn't offering a stationary target, so a single kill shot is nearly impossible. Grizzly bears are amazingly fast at shorter distances...

There are a host of other reasons why you shouldn't carry a gun of any type if you don't have the skills necessary to disable or kill the animal on the first shot.