Primary weapon would be a hardwood throwing stick, shaped along the lines of a boomerang. I would have a sling handy just in case their were some fowl that were out of distance of the stick. Knife is the tool of choice.
Besides that, I'd set a lot of foot-hold snares along deer trails and try to start forming fish hooks as well.
I've made a fair number of solid long and short bows, and dozens of arrows, however, with the time invested in properly seasoning the wood and ensuring a good tiller, I could probably walk to civilization from almost anywhere in the same amount of time. If I could bring a bow with me, that's another story.
Also, on Bear, I would blame the producers more than him. They put out a show that people want to watch. He really has done a lot with the SAS reserves and climbing Everest after a debilitating back injury. But TV is rarely the best source for practical knowledge regardless.