I don't know how much rubber mulch it takes to stop a - Hey, just what caliber are we talking about? - bullet, but that is a popular material for indoor shooting ranges these days.
There was once a pistol/rimfire bullet trap comprising a box full of gravel. Nicely made, of course, but functionally a box of gravel. The heavy cardboard front face would take a fair amount of shooting before it got ragged enough to leak gravel, and was readily replaceable. A piece of heavy rubber, like conveyor belt, would last even longer.
So I visualize the barrel laid horizontal in a sawbuck type cradle, full of (something) and capped with a cheap and/or self sealing material.