"Bear Caliber" leaves a lot of room for discussion, and a big hole that needs a little more information to pin it down. Three to four hundred pound Black Bear, five or six hundred pound Grizzlie, or eight to one thousand pound Brown Bear?
Black Bear, 45-70(300gr), 30-06(165gr), 30-30(150), .35 Remington(200), or .270(150gr).
Grizzlie, 45-70(400gr), 30-06(200gr), .35 Whelen(250gr), .338-06(225gr), .350 Rem Mag(225gr), .300 Win Mag(220gr).
Brown Bear, .450 Marlin(400gr), .375 H&H(300gr), .338Win Mag(250gr), .416Rigby(400gr), .458 Win Mag(500gr).
This is what I personnally would want the people I was backing up to be carrying.
Gun is unimportant, since I usually carry single shots, I only expect to get one shot anyway. I usually carry a TCR, or Handi Rifle. Sometimes I carry one of my Ruger M-77s, or a Mauser.