Am I truly the only person hereabouts who ever won a war against Bermuda grass?!
I have hated Bermuda grass since high school, since my father assigned me the responsibility of trimming off the runners because he wanted a green "carpet" of Bermuda grass in Tampa, Florida. (He, of course, couldn't be bothered to maintain his own stupid... never mind...)
Fast forward many years.
When DH and I lived in Berkeley, I did weight training and a lot of distance bicycle riding. Neither the Bicycle Accident nor the Car Accident had yet occurred, so I could do heavy physical work for hours at a time.
One day, I had just HAD IT UP TO HERE (ich hatte die Nase voll gehabt, in German) with Bermuda grass. Our yard was small, maybe 10' or 15' x 20', but even that was way too much Bermuda grass
It was going down.
I had a plan. It sounded wacky, even to me, but I didn't see why it wouldn't work. All it needed was a lot OF work....
I rummaged around in the garage and found some 1x2s, wood glue, a staple gun, and some half-inch hardware cloth. I had never seen one, but I made a compost screen (it lasted from the early '80s until 2008, when I replaced the 1x2s). I rolled the wheelbarrow out to the front yard, carried the shovel and the square spade out there, root beer, compost screen, work gloves, and got started.
I dug the stuff out and threw it on top of the screen. Anything that went through the screen was returned to the ground; anything too large to pass went into the city's approved yard pick-up bags.
Yes, ladies and gentlemen, yes...I sifted my front-yard dirt. Something like 300 cubic feet, give or take--there were oddly shaped places beyond the basic rectangle where I dug out the dirt and Bermuda grass, and I didn't always have to go a foot down; sometimes I got away with 10 inches or so.
I did this screening of Bermuda grass in maybe 1983. Given my personal history, this date isn't off by more than one year in either direction. We sold that house in 1997 and moved to where we are now. The Bermuda grass stayed gone.
Now, I realize that, in most parts of the United States, yards are much larger than 15' x 20'. So I recommend a combination of the above technique and the technique I used against invasive bamboo at the same Berkeley house: metal flashing usually used as a pretty divider between planting beds, shoved straight down into the ground as deeply as it can go, so that only half an inch or so of it is visible (you do NOT want to lose track of this stuff!).
Work on the Bermuda grass in pre-determined plots of whatever size you can manage without overdoing it. Mark these plots off with the flashing when you're done so that roots from any remaining Bermuda grass won't re-invade.
Plant something nice, something non-invasive that you *want* in the newly cleared plot. Nature abhors a vacuum; let her know your preference before she sends random weed seeds your way!
Best wishes for success against this vile plant.
Sunset Zone 17, USDA Zone 9