Removing and keeping Bermuda grass out of prepared beds is an oft discussed topic. Try some searching, or save the reading time and go to digging instead. Physical removal, physical barriers, weedeaters are your weapons. You can and should mulch your bare soil, but don't count on that to be a single pointed attack...or at least don't expect much success.
As organic1 mentioned, Bermuda grass is sometimes considered a weed, in addition to being a lawn covering and it is aggressive. You have to be more aggressive.