Here in the UK, we call Bermuda Grass, "Couch Grass".
Below is a link describing how to deal with it organically.
Seems the best way, if you take it one area at a time, when you have to initially dig a no-till/no-dig garden anyway:
http://www.gardenaction.co.uk/allotment/couch-grass-1.asp
Once you have cleared the area, and trenched round it, as soon as any little bits remaining grow back, you could treat them with a weed wand, which is also chemical free.
You don't burn it right out; it works by altering the DNA of weeds so that they die above and below the surface.
It also has a small working area, so you could take out Bermuda grass which is growing BETWEEN your plants, with no backache.