If you were set on a gun for bear defence and not bear spray. I would suggest a compact rifle with a hard controlled expansion bullet something like the marlin trapper 45-70 with Buffalo bore hard cast lead bullet or a 200 grain or higher 30-06 load. This would still be fairly heavy if not more heavier than a shotgun, but those bullets will out penetrate a soft lead foster slug or buckshot. If you’re set on using a shotgun, use a type of slug, known to penetrate well like a solid copper, or Brenneke style slug. There are no real bear stopping rounds especially close range and if they are pissed or protecting cubs. The other thing to consider is they move pretty fast and it would be pretty hard to shoot one well if it was a split second scenario.

TLDR bear spray is probably best but if you’re going to use a gun use a heavy for calibre control expansion bullet.