Ask Mr. Smarty Plants

Bermuda grass (Cynodon dactylon) is not a native grass and is quite an invasive species. It is not from Bermuda but was presumed to have arrived in North America from there. It is a warm climate grass, fast-growing and tough. Its heat and drought tolerance enable it to survive well in the southern states where few other grasses survive. It is coarse-bladed and is described on the Wikipedia.org website as highly aggressive, crowding out most other grasses and invading other habitats, and has become a hard-to-eradicate weed in some areas.
In a Texas AgriLife Extension bulletin, “Bermudagrass Varieties, Hybrids and Blends for Texas” by Vanessa Corriher and Larry A. Redmon, they write that Bermudagrass (Cynodon dactylon) is native to southeast Africa. The earliest mention of bermudagrass comes from the diary of Thomas Spalding, owner of Sapeloe Island, Georgia and a prominent antebellum agriculturalist. Found in his diary was the following entry: “Bermudagrass was brought to Savannah in 1751 by Governor Henry Ellis.” He went on to say that “If ever this becomes a grazing country it must be through the instrumentality of this grass.” Writers as early as 1807 referred to bermudagrass as one of the most important grasses in the South at the time. Thus, bermudagrass has been a part of southern agriculture for at least 250 years. Hybrid bermudagrass with improved productive capability and nutritive value has played an important role in livestock production across the southern US for nearly 60 years with the introduction of ‘Coastal’ in 1943.
Bermudagrass is a warm-season perennial grass that spreads by rhizomes (underground stems) and/or stolons (horizontal aboveground stems). The grass tolerates a wide range of soil types and soil pH values, thus it is adapted to most of the southern U.S.
Now on to your question about native grasses for Georgia lawns.  Buffalograss (Bouteloua dactyloides) is native to Georgia and we have some good information about this native grass on our website.  It produces a soft, fine-leaved, low-maintenance, drought-tolerant turf grass that can be mowed.
Buffalograss is a soft, gray-green or blue-green, perennial turf grass which grows 3-12 inches if left unmowed and spreads by rhizomes. This long-lived, warm-season, sod-forming grass has curly leaf blades, slender stems, and compact seed heads.
One of very few drought-tolerant North American grasses suitable for lawn use, and the only one widely available, Buffalograss has become very popular since the late 1980s. (Two other drought-tolerant native lawn grasses are Blue Grama/B. gracilis and Curly Mesquite Grass/Hilaria belangeri.) Buffalograss does best in clay loam, where it can survive on as little as one and a half inches of rainfall per month. In areas with even less rainfall, Buffalograss is sometimes mixed with the more drought-tolerant Blue Grama (B. gracilis) to insure solid color through the dry season. Cultivars 'Texoka' and 'Comanche' were bred for forage and can reach 12 inches. '609', 'Prairie', and 'Stampede' are lawn selections. Stampede doesn’t get taller than 4 inches. These cultivars have been selected for lawn use and are mostly male strains so there won’t be seedheads produced. Buffalograss lawns can be mowed or left to billow softly in the wind.  A buffalograss lawn requires only one and a half inches of rain per month to stay green and will go dormant during droughts and in winter.
There are a great many native grasses for Georgia that would be excellent plants for your garden or a wildflower meadow and Gary Wade (and friends) at UGA extension have an excellent webpage discussing these plants if you want to learn more about them. It is Native Plants for Georgia Part IV: Grasses and Sedges.  These aren’t suitable plants for a mown lawn though.