Bermuda grass (Cynodon dactylon) is a great lawn grass for many areas. It is drought tolerant and establishes well in almost any soil conditions. It can, however, be very invasive. Its vast underground and aboveground spreading systems -- stolons and rhizomes -- make Bermuda grass difficult to eliminate from the garden. Having around desirable plants that need to remain undisturbed makes the process more difficult.
Water the area well before removing Bermuda grass.
Remove the runners. Bermuda grass covers bare ground quickly, which makes it a good lawn grass. That same quality also makes it invasive. Once it has crossed over into a flower bed it can be next to impossible to get rid of. Put on gardening gloves and pull out the runners.
Dig up the earth and remove each bit of underground rhizome. Any root left whatsoever will start a new Bermuda grass plant.
If the runners are very deep in clay soil and cannot be pulled out, you can use grass-specific herbicides that will not kill other plants, like Grass-b-gone, Over the Top, Ornamec and Vantage. After the grass has died pull what remains out. Repeat the process for any new shoots that crop up.
Isolate your lawn from your flower beds and garden. You first want to put up a good barrier between your beds and your lawn. Use black polyethylene barrier over the grass and add plastic edging around the flower bed. Do not remove the polyethylene for at least six to eight weeks during the growth season of the Bermuda grass. Keep the lawn trimmed back at the edge, so stolons don't cross over it.