Bermuda grass sucks. About 5 years ago I did the same thing you're thinking about doing I build a raised bed I put cardboard down it wasn't two feet deep it was about a foot. I planted a whole bunch of strawberries in it and by the end of the summer the Bermudagrass was the so thick nothing would grow but the grass. I'm dug out most of the dirt and replaced it and the next summer the Bermudagrass came back just as thick. So I ended up spraying Roundup in it. Which killed most of it even though that was several several years ago I have never planted food in there again it became a flower bed. Last summer I bought a weed torch which really helped but I had to use it almost everyday. Soon as I saw one little blade come out of the ground I torched it. So I'm watching this question to see if there are any good ways to really kill this stuff. I don't think suffocating it will work because it runs and Vines under the ground so if it comes up somewhere else it's still alive.
