I have deep and unyielding hatred for Bermuda grass. It was my duty, during high school, to maintain my father's Bermuda-grass lawn by cutting all the runners by hand....and, of course, in California, it's very invasive. But I successfully removed it (and it stayed gone for over 10 years) at our house in Berkeley.
This does *not* look like Bermuda grass, for a number of reasons.
I'm not familiar with St. Augustine grass.
However, I don't think that matters in this case, because I think you have what I am *now* dealing with here in El Cerrito: kikuyu grass. This monster behaves something like a cross between kudzu and Bermuda grass: it grows beneath concrete, into the dark underneath the sidewalk, from any fragment of the plant. It is classified as "noxious and invasive" in the State of California.
When you dig it up, get as much of the root as you can, and just keep after it. Soon after rain is a good time to attack it, because the roots will forsake the ground more easily.
Best wishes, and I'm sorry.
Sunset Zone 17, USDA Zone 9