Yes, the trick is to keep the Bermuda grass out of the cleared area. We plan to cut in a border of flat, 6 inch galvanized steel. That will prevent the roots from spreading under ground. Then, we need to make sure the above ground runners stay clipped, so they can't spread over the top. I'm also planning to keep at least a mower's width of cover crop/grass inside the garden fencing, so we can keep it mowed, and weed free.
I knooow! Bermuda grass (aka coastal hay) can be a good thing - we feed it to our goats. Or, it can be a PITA, if trying to grow a vegetable garden. Last year we tried clearing a 15×15' area for vegetables. Very quickly, the Bermuda grew back. We figure the best way to get rid of it is to cut below the roots & move the sod out in the back pasture, to fill all the holes the previous owner left, when they pulled out trees.You have my deepest sympathy for all that bermuda grass. That really was a lot of hard work!
I battled it for years then decided it was just easier to get several states away. Worked like a charm, haha.
Best wishes for a terrific garden, it looks like a great spot!