My only experience with recoil is with 12 & 20 gauge shotguns as well as 30-06. And I don’t like the recoil. NY state allows any center fire rifle & 20ga or larger shotguns. Based on that, my 1st thought was a 22 Hornet, but I wouldn’t trust that on a bear!
I haven't shot any bears, but I can tell you cartridges with a lot less recoil than a 30-06 are plenty for deer.