If you are using round-up yes--but get a large piece of cardboard and hold it on the garden side so you don't spray your vegetables.

Round-up only kills what it lands on and is neutralized when it hits the ground. I spray it every year around my perennials to kill the quack grass using the cardboard. In fact I use the sign the builders put up on our lawn when we had our windows changed.

I've never lost a plant and plant my annuals after the grass dies. It will take a couple of weeks to work. What it does is actually grow the plant to death. Spray when you are going to have a couple of days of sunshine.

I'm not sure it will take care of your bermuda grass past the spray area but it will give it ground to grow in besides your garden