An aquaintance shot a bear with a .222 Remington once.
I shot severqal bears with a 243. This was on Vancouver Island and they were mostly very close neck shots though I did a face on chest shot once and had to track a wounded bear, but did recover it.
But once I tried a broadside lung shot on a very small bear at 20 yards. It dropped, reared and puked then got up and ran away, never to be seen again.
I switched to a 30 calibre.
22-250? My advice is use one only if you are close enough to guarantee a neck or spine shot. I wouldn't trust it on a body shot.