Years ago when I was wanting a new bed, I knew the Bermuda was going to be a problem. I wet the area and put cardboard down, no cracks and thought the Bermuda would even push through with rocks on top. The only thing I could think of to weight it down, and get hot enough to burn the grass, left over roof shingles. They worked like a charm. If you don't have any or enough. Decades ago when I was teaching stores gladly donated supplies for school gardens but parents might be looking to get rid of the shingles also
Good luck
