Bermudagrass is a beast. (Cynodon dactylon and friends) A warm-season (summer) sod-forming grass with incredibly aggressive and tough above- and below-ground rhzomes/stolons. It's great if you want it, but hellish when you don't.
Removing it by hand form my veg garden has confirmed the lore that plenty of its rhizomes occur well below a foot underground. It's a beast.
A search of the net and the library for ways to remove Bermudagrass provides a few options. (1. Spray repeatedly. 2. Dig by hand for ages and ages, removing all living material. (I've done this) 3. Fry it under plastic tarp for at least a year. 4. Smother it with tightly pinned layers of weed fabric.
Well, none of these were going to work very well for my garden client, but we almost resigned on one... until a miracle revealed itself:
This particular lawn of Bermudagrass mostly had rhizomes within the top two inches, like a normal sod-grass. Wierd. For the records, a few spots were indeed deeper. But not much. We've already dug most of those out. So, miracle of miracles, a rented sod cutter, set to two inches, did a bang up job of decapitating this Hydra. I want to type the word again: Miracle. What profound Providence.
Now we are moving on with the dryland/native/unwatered garden.
Technique #5 for Bermudagrass removal: Don't assume that your patch of Bermudagrass has its roots wrapped around the subway system in Shanghai: Actually check if the rhizomes are as deep as feared.
I'm humbled, again, to an old adage: Assume nothing.