Polar bear? Let's see now, big teeth, big claws, maybe 1500lbs. +/-, and could be a mean disposition.
So, 243Win., 24cal. with 100gr. bullet doing maybe 2900-3000fps........ ?

Or, 45/70, 45cal. with 350gr. bullet doing about 2100 - 2200fps! (Buffalo Bore or Griz ammo).

Hmmm, what to use? Decisions, decisions.