To remove the Bermuda grass I use a trimmer and cut back all the grass to the ground. Then I till up the soil multiple times. After each run with the tiller I rake up the roots and stolons for collection and dump them. The remains never go in the compost bin as all it takes is one little piece of uncomposted Bermuda grass to wreak havoc later. I repeat the process until as much of the grass is out as possible. It will come back, but this process makes a major dent in it. The disadvantage of this method is that the tiller cuts the Bermuda grass into smaller pieces which can resprout. In the spring before planting I'll need to repeat the process and then again in the fall. This probably will not eliminate it but should keep it under control. Every piece of Bermuda grass root that is removed will mean a smaller problem later.
Another method for removing Bermuda grass involves completely removing the soil. To do that you need to remove at least 6 inches of soil to be sure all the roots are accounted for. That is a lot of soil to remove so I prefer to use the tilling method to leave the majority of the soil in place.
Solarizing is another method. A plastic sheet can cover the area which increases the heat underneath and reduces moisture in the soil which will eventually kill off Bermuda grass. Solarizing Bermuda grass can take several weeks to accomplish.