Why not just make him say "-kuma" at the end of the line? I mean, it's not really a pun, it's a verbal tic, and it just becomes like Kongou's -DESS or Inazuma's -nanodesu.
Okay, let's head out!OUCH!I know beary well!You will!
Thank you!Off we go!TALLY HO!MIE!
WAKE UP!Mr. Bear...
Do you know the Mountain Witch's house?Mr. Bear, what kind of youkai are you?ONIGUMA
Even carrying 10 people, they do not buckle.
A bear youkai said to be capable of moving massive boulders with ease.Come ride on my bear back!
I'll bear you there!The Oni Bear-san.An Oniguma, rawr!