I see this is old, but perhaps it is not fixed on PS4? It just happened to me. I went back in the trapper's cabin, the camp office, cabin, all 3 logging camp trailers, and the cabin near the bear's cave. The bear's footprints led into the cave, but he was not there. I restarted and didn't enter any buildings and finished the challenge no problem. The bear also runs away at the northern river access without having to shoot him.
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