For a portable bullet trap, I use a deep plastic bucket w/lid filled with rubber mulch packed firmly. I haven't had any handgun round penetrate deeply enough yet. At the most they seem to stop at the 12 inch mark. If you're thinking of using it for rifle also I would put a steel plate, maybe 3/8 - 1/4 inch in the bottom.
Those buckets that kitty litter comes in would probably work, you always see those being throw out in the trash, or check with your local grocery store, those with an in-store bakery. I know you can get them there and replacement lids.