Alright, here are some early concepts freshly scanned from my sketch book:

I’ve been futzing around with a few ideas in this picture. I have the basic concept down but I’m trying to settle on a motif for the bear. It’s really eclectic right now. I imagine the speedo to be red with white trim but I think those’ll evolve into board shorts and the skateboarding style kneepads will merge into the main design. Ignore the steampunky shin guard… that was a poor decision. As for the championship wrestling belt: it just fit with the speedo.
The big thing strapped to his back is a giant salt water tank to hold the shark. I imagine the bear wielding the shark like some kind of long arm (not a pistol) so the shark’d have to be pretty big proportianally. The tank has a hose on it so the bear can spray down the shark during long firefights to let him breathe a bit. I also imagine some cool attacks where the bear leaves the shark in the tank and just throws enemies into the tank and lets the shark eat them, allowing the bear to multi-task in close combat situations.
Here’s the shark: 
I love his grumpy face, so the basic breed of shark is staying the same. The bit in his mouth in the second design is like a bit for a horse, this would couple with a strap tied around the shark’s tail, giving him a holding strap like on a rifle.
The premise of combat is as such. The bear operates the pump action, which can mess with the sharks digestive system. He then can pull back on Shark’s dorsal fin to make Shark vomit up anything he’s eaten (tables, people, liscence plates, computers) as a projectile attack. Also the shark makes a mean close combat weapon with all the biting and such.
The duo would be a tenuous alliance, I imagine Shark saying to Bear “When I run out of enemies to eat, I’m going to turn on you next”
Comments, suggestions and crits are always super welcome!