Answer: Bermuda grass covers bare ground quickly which makes it a good lawn grass. That same quality also makes it invasive. It travels by runners, called stolons, that are root-stems and which advance forward, putting down new roots. Once it has crossed over into a flower bed it can be next to impossible to get rid of.
You first want to put up a good barrier between your beds and your lawn. I recommend at least a foot of hardwood mulch with plastic edging buried about six inches. Keep the lawn trimmed back to the edge of the mulch line so stolons don't cross over it. It will be like a "demilitarized zone between your lawn and flower beds and if you see Bermuda grass stolons starting to cross it you can kill them.
If Bermuda grass does cross over into the garden bed you need to remove the stolon root and all. Wet the flower bed down well and using gloves pull up the runners, root and all. Any root left whatsoever will start an new Bermuda grass plant. If the runners are very deep in clay soil and cannot be pulled out get a painters wool glove and wearing a second rubber glove place the painters glove on your hand and douse with Roundup week killer at the recommended dilution.
Run you painter's glove with weed killer on it across the shaft of all the grass in your flower bed, careful not to touch garden plants.
After the grass has died pull what remains out. Repeat the process for any new shoots that crop up.
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