RE: 243 for bear?
It' s not the best choice by any means, but it will work. I' d personally feel much more comfortable with, say, the .257 Roberts with 120gr bullets or the .260 Rem with 140gr bullets, both of the premium variety, such as the Nosler Partition. Both offer more penetration and killing power with little increase in felt recoil.
I have a buddy who has taken many blackies with his .257 Roberts, including one bruiser that weighed over 400 lbs. He gets close (under 200 yards) and only pulls the trigger when he is sure he can hit the vitals. It has worked like a charm every time. One other thing: He also owns a .243 Win and has never used it on black bear.