Remove (or kill by spraying with Roundup) the crabgrass and weeds in each bed. (If you used Roundup, wait a week or so to make certain everything you sprayed is dying.) Cover the entire bed with newspaper several sheets thick; wet it thoroughly, then cover with mulch.

Seeds will still blow into the bed or be buried by squirrels, and some will sprout even in the deepest mulch. If you're still doing more weeding than you want to, consider using a pre-emergent.

Also, be aware that the Bermuda grass is going to be a constant invader at the edges, and keep on top of edging it to keep it out. Personally, I would never use bermuda grass unless it was completely contained by hardscape at all edges.

Agree with above advice, but, if you do the newspaper (i use cardboard), no need to use the roundup.

You can consider just simply going in with the Roundup, and forgo adding more mulch, depending on the state of the mulch.

Agree, COMPLETELY, about the Bermuda grass (there are those who hate it and those who love it, but,) BUT... it WILL invade your beds unless a deep hard edge is put around it.