Excellent advice. A barrier can also be weed-trimmed against, severing any runners that try to jump over it.
When mowing, aim the chute away from beds if the grass has any seeds on it.
For existing patches, you could pull the mulch back, lay cardboard on it, cover thickly with mulch, to weigh it down and block all of the light. That should be the end of the grass, as long as it's undisturbed until the grass is truly dead, and covers the patch completely. If seams are necessary, overlap at least 6" so grass can't find the crack to exploit. If left alone, the cardboard will decompose and does not need to be removed. Even works wiregrass, and bahiagrass. Our yard has those and others, not hard to keep out of beds once eliminated.
