I would sell the katana and buy lots and lots of peanuts and other food that elephants enjoy. Then I would befriend the elephant and tell him that if he can help me with my bear and lion problem, I will feed him peanuts and whatever else it is that elephants like. If the elephant ever turned on me, I would send him to Norway. Problem solved.
Best idea so far.

Katana can easily damage a bear. It's just that there's no way you'd be able to stop the bear once it's bent on killing you. You wouldn't be able cut a leg off. You'd have to be pretty miraculous swordsman. Considering you'd need a perfect angle and it shouldn't change during the process. And swipes are circular in motion. So no go. If you manage harm it you can be sure it's going to come to finish you off. If you had ever hunted bears you'd know. When they're injured tehy won't stop until either of you is dead. They are not as dumb as you might think. They might even retreat and ambush you if their wounds aren't that severe. Not sure how they'd think about someone wielding a sword but they've done that against hunters. Oh and recovering from what have been full strenght blows? Yeah, I'd like to see you get up after that. Besides, a bear is faster than you are so the whole idea of making hits without taking any is absurd.
Concerning the Katana fanboyism...
It's not actually even a very good sword. You can't block with it because it's so thin. The shape very aggressive and leaves the user exposed. The whole fighting style with it depends on the owner being overly aggressive. If you accidentally or by dire need make a direct block with it the hard edge will crack from there and after a few of those cracks the sword becomes dangerously weak and easy to break.
The bad quality of Japanese iron ore forced them to make swords formed like that since the regular type swords made from it couldn't last.
Ironic that the Japanese learned how to make steel from the europeans around 1800 while chinese had been making steel for almost 2000 years.
Oh yeah, how many prisoners do you think the japanese had, hmmm? Now how many katanas did they have, hmmm?