What I did is put a layer of cardboard and then a few inches of mulch. This year just a few sprigs of Bermuda grass came up. I put another layer of cardboard and more mulch. It really does work. You could use RoundUp and kill weeds before the cardboard goes down too. I would hold a big piece of cardboard in front to keep it off any plants you want to keep. Wait a few days after spraying and then do the cardboard. I can't believe how well this worked!

All my garden beds were mulched with over-lapping pieces of recycled corrugated cardboard topped with 4-6 inches of shredded bark mulch. Cuts down about 95% of the weeds and lasts a number of years. It's organic, looks natural and eliminates all weeding other than at the outside edges of the cardboard.

FYI - at first I used multiple layers of newspaper under the mulch but found the cardboard worked much better.

Oh, yeah, almost forgot to mention...worms LOVE cardboard.

Sounds great! Now to find enough sources of cardboard.

Cardboard should be sufficient. Any weeds that grow will have come up between the cardboard edges. I've done that. You could top the cardboard with black plastic to be sure. Weeds are determined, but not unsmotherable.