The damn bishop's weed made its way up under the soil and up through two of my raised bed boxes last summer, pretty much taking over each 3 X 3 box.

I have in the garage a never-used roll of bamboo barrier - a thick roll of black plastic that I was going to use vertically to keep running bamboo contained (but I decided not to buy the bamboo). So I was wondering if I could remove the soil from the weed-infested beds, shift out the bishop's weed, put overlapping squares of the black plastic down on the bottom, and then put the soil back (it's good stuff, amended every year, mixed with coir and pumice).

Or alternatively, I could put piles of newspaper on the bottom... (I'm a little afraid of our wet winters and no drainage if I use the black plastic).

Any thoughts about either of these attempted remedies - or other solutions?