Bermuda grass (Cynodon dactylon) is my favorite weed to eradicate. In my experience, it's one of the easiest pernicious weeds to get rid of!
I've eliminated this perennial grass at more than half a dozen organic community garden plots and paths in the past couple decades. It took less than one season in every case, plus ongoing diligence. I kept Bermuda grass out of one garden plot and its surrounding paths for over 15 years even though it was rampant in neighboring plots.
In each case, I got rid of Bermuda grass by scraping the surface to get rid of above-ground stems, or stolons, and digging up any obvious below-ground stems, or rhizomes. In paths, I added overlapping layers of newspaper or cardboard, then piled on 6-12” of mulch. If any of it struggled through, it was weakened and easy to pull, and for the worst infestations I checked at least weekly. In garden soil, I learned to recognize bright-white propagules -- any segments of stolon or rhizome -- and got rid of them as I moved soil or forked in compost.
As a lawn grass, Bermuda can be planted by chopping up rhizomes and incorporating them into the soil. So if you rototill in an area that has Bermuda grass, you are actually replanting it! Each segment becomes a new plant.
It's especially easy to pull up Bermuda grass when the soil is moistened by winter rainfall. If I find a dense patch, I dig under it with a hori hori from a couple directions, then grab the whole clump of weed and soil and shake it. The remaining white rhizomes stand out against the dark soil. Grab one end, tug slightly, and see if you can prise ever-longer rhizome pieces out of the ground. If it's growing in mulch, it's even easier to pull out stolons and rhizomes.
For more information, see https://ipm.ucanr.edu/pmg/pestnotes/pn7453.html
The worst infestations I found were under weed cloth. Bermuda grows happily through and under the weed “barrier.” In California's dry summers, the weed cloth maintains a layer of moisture under the mulch and helps it flourish.