Because you asked about the permaculture way, I'll suggest... Forest garden! Bermuda grass likes sun. When you have all the niches filled with a plant you want, taking all the sun, it has a harder time growing. We are trying to maintain our vegetable gardens in a perpetual state of annual plants, rather than woody forests. What invaders/ primary colonizers/ "pioneer" species do is take that kind of land over in the first step to becoming a forest (depending on your bioregion). Permaculturists, of course, can want vegetable gardens. But those won't be permanent in the same way a forest garden is. It will be constant work/love maintaining that unnatural state: weeding with good sharp tools, planting vigorous crops and cover crops to compete for the light, mulching to make lighter soil that is easier to weed, placng physical barriers that block the stolons from invading, spending time with your garden.
