It was good enough for Grandpa so unless bears have gotten considerably tougher in the last 75 years I would say you are good to go. Just make sure you know where to shoot the bear and that your marksmanship is up to it.
My step father had to rescue a buddy of his who emptied 4 rounds of 300 Savage into a black bear and then went up a tree. The bear was going up after him when my step father shot it dead with a Stevens single shot 25-20. I still have that gun but rechambered for the WCF round and I only use it for ground squirrels. 30-30 was the gun of choice for my step father after that but he inherited the 300 Savage for deer hunting. His friend found other pursuits like flying and drinking. He considered it safer than bear hunting.
The link is for bow hunters but everything is applicable. I had another link for frontal shots but lost it, sorry bout that.