While regular beartraps do not work, LARGE ones do.

Place the traps in a line and scatter some in the surrounding area, then line up the bear to parallel with the trap line, and start shooting tranqs.

This will cause them to slowly work their way through the traps, and all you need to do is keep shooting.

If it gets down to the last trap, hop on an Argentavis and fly high up, then away to a base (I find they will follow you very far).