I ain't PS, haven't hunted brown bear, and only have a little experience with the 9.3x62, but that never stops anybody on the internet.
I think my first choice for an action would be the Ruger.
The 9.3x62 seems a very well mannered case--no belt, no steep shoulder, not high pressure. So I think it should feed well and extract smoothly in virtually any action you use. My favorite LH hunting rifle actions are the Winchester, Remington, and Ruger. Stainless Win 70s are way too spendy, Remington's are probably the standard against which all others are judged, but stainless/standard boltface actions are not uber common. For a bear gun, I think the scope mounting system on the Ruger would be hard to beat, and they are rugged actions.
