Unfortunately, bermudagrass is very tough to get rid of.
The first step is to kill it with repeat (three or more) applications of Roundup or another nonselective herbicide. Roundup kills everything it touches, so it will also kill bluegrass and rye. If this is a large portion of your lawn, that means you'll have to kill a large portion of your lawn. Follow the package directions exactly. Once the bermudagrass is dead, dig up the roots as well to make sure it doesn't return next year. Dig it up to a depth of 1-2 inches. For large areas, use a sod cutter.Then spread with top-quality topsoil or compost to replace the soil you removed and reseed or resod. The good news is that fall is the ideal time to reseed or resod a lawn, setting you up for a beautiful lawn next spring.