These type thing's have no right answer but rather a lot of answer's. Anything from say a 6.5 on up will work for what she need's. smaller the cal, less the recoil. Lighter the bullet, less the recoil. Now, haven't a clue about factory ammo but in 6.5 as light as I'd go is 120gr. 7mm is 140gr and 30 would be 150gr. Your probably gonna need a rifle unless you plan on throwing the bullet's. Check out the inexpensive kit rifle's, new rifle generally with a plastic stock and an inexpensive scope, normally a 3-9x. I think Ruger makes one, know Savage and Mossberg do. Only one I ever bought was the Mossberg Patriot and without a scope and plastic stock at the time it was $299. I don't recall the price with the scope. I think it does come in 6.5 Creedmoor, 7mm-08 and 308, I'd suggest the 7mm-08 in it. Supposed to be fairly easy on recoil and should be easy to find in 140gr loads. 6.5 Creedmoor will probably be harder to find ammo for and 308 is easy to find ammo for but it will also increase recoil some. I have a 6.5x55, similar to the Creedmoor and recoil is not bad at all. Ammo is easy to find because I don't buy factory ammo, I reload every thing. In the past I had 7x57's which are close to the 7mm-08. Recoil is not bad at all. 308 Is a favorite of mine but in a bolt action recoil will go up a bit. How much you can take, no one here can tell you! Put's us back at the 6.5 Creedmoor! There are those that will suggest the 243. It would work but there are a lot better answer's! You could kill the bear with a 22 rim fire but there are lot better answer's. On the world record grizzly killed with the 22 long rifle, I read about it a while back and the shot in in position that suited her she shot it in a soft spot below the ear just a bit and it went right down. The story I read was not in self defense. The shot was carefully placed where she knew it would drop the bear. After the shot she went to it and fired several more shot's into it. I doubt many of us here have the cool to pull off something like that! Which ever story is correct, I don't know but, bears can be cleanly killed with pretty much anything is all your stars aline right! But there are better answer's and for me they start at 6.5 caliber.
I do not use premium bullet's on anything, not necessary but in your case it may be. I assume that solid bullet is the law every where in California. Use a solid copper bullet in that case. Be sure it is not a full metal jacket, that is not a solid copper bullet! Most importantly, before you try this, practice with the rifle you end up with and learn where to place your shot's. A black bear will likely be interested in avoiding you but who knows if it's wounded. Learn to shoot well and where to place your shots. Probably the best answer for you in your situation is to have someone that knows how to do this and has the rifle come in and do it for you. That guy would not be hard to find. Local sporting good's store could probably set you right up!