Bermuda grass is a very sturdy and hardy grass that is favored for its toughness. It's often planted as a lawn grass for this characteristic, especially in warm-weather climates. It is a pretty hard plant to kill, but your garden is definitely not the right place for it. This can pose a problem, since the most common way to kill Bermuda grass is with herbicides that contain harsh chemicals you probably don't want near your garden. If you need to stop an invasion of Bermuda grass, and you don't want to use chemicals, your best chance is to use the old household standby, vinegar. Alternately, you can use boiling water, which kills weeds and also Bermuda grass.
Mix a 20 percent vinegar solution in a jug or bucket. This means for every cup of vinegar, you should add four cups of water. Pour the solution into a hand spray bottle for a small infestation or a garden sprayer for a large area.
Temporarily cover plants you don't want to injure or kill, such as your garden plants, with heavy plastic sheeting, to keep the vinegar spray off. Spray the vinegar on the Bermuda grass, keeping the spray close to the ground to avoid spraying other plants growing in your garden.
Wait until the vinegar dries before repeating the application. The first time, it may only kill the top inch or so of the grass, so at least a second spraying is a good idea. Spray using the same method as before. Vinegar should kill Bermuda grass effectively in 1 to 2 days from the first application.
An alternative method is to use boiling water on the grass to kill it. Just boil up some water in a kettle or pot, and pour it directly onto the grass, literally boiling it to death. To target small areas of Bermuda grass, cut a milk jug in half and set the top half over the grass. Then pour the boiling water into the mouth of the milk jug.
Dig up or pull up the dead Bermuda grass once it is brown and dried. You can pull it out by hand, but use a spade or hoe to get underneath the soil at the grass's roots, and chop them away to be sure the grass does not regrow.