the bush...like Australia? Probably screwed there but if you mean the wild than use a snare with your shoelaces
Just do the classic deadfall trap, use a wire/string trigger though. I once made a fucking awesome trap while I was bored on a backpacking trip, I used an almond for bait, and when the squril would pull on it, it would release a trigger which would drop a rock that I used as a counter weight, and the squril would get trapped inside a sleeping bag case and lifted up 5 ft into the air. Fucking hilarious.(Didn't eat it, I'm veggietarian.)