I have no experience on bears, but I did shoot some game with a 243 equivalent, a 27" bbl 6x47mm ( 222 magnum necked up to 6mm) I was recovering from a neck surgery, and I wanted as little recoil as possible. I used the Barnes 85gr XBT. I shot an axis doe at 75yds, complete pass through, dropped on the spot (behind the shoulder shot) I shot a big axis buck twice, first time was a hard angle (hey, those spots had him camoflaged in the shade!) finished him at 15yds w/2nd.
Now, on the same hunt, I made a deal on a Simitar Horned Oryx. The guide was 'semi-reluctant" to let me use the little rifle, but I had hunted with him many times, I told him I'd neck shoot the thing. We got on a small group, followed them for about a half mile, couldn't get closer than 184yds (lasered) I leaned against a small tree, still on my knees and plugged him toward the base of the neck, broadside, complete pass through, 1" exit hole. He dropped like a sack of dirt, no twitch either! I walked up to about 75yds form him , and gave an insurance shot (those 41" horns can kill you!) his brisket/legs were facing me, I put it through his heart, it stopped in the spine, breaking it. It weighed 83gr later! That tough hide and heavy muscles helped the little 86gr expand.
I've also used a 220 Swift with 55gr Bearclaw bullets right after that neck surgery, shot mule deer , axis and blackbuck antelope. I like to experiment! ha Here in Utah, I know several guys who use 243s, 6mm remingtons and 240 Weatherbys for deer/elk. I agree that the best use of small caliber rifles (with good bullets) is to use them like a sniper...surgical placement. If you can discipline yourself to do that, they work swell.
Smallest I use now on game is a .270, just because I have a sweet Belgium BAR in one.