There is a big temptation to over seed a Bermuda grass lawn, however you must understand the risks before you chose to overseed. In this video Doc talks about these risks of over seeding Bermuda grass and what you need to know. Each variety of Bermuda Grass will have a different texture, color, growth pattern, and other characteristics that may not match your current lawn.
Overseeding Bermuda lawns should be as a LAST resort. If you care for your lawn well you can push it and make it fill in.