In the areas where I've gotten it out I have had very little bermuda trying to come back...although after the winter rains everything else wants to grow!
I have used Round-Up in the past...but I'm trying to do it without the chemicals in this section of the field, both because I think it's the right thing to do, and because I may at some point want to grow some vegetables again (in part of it). Fortunately, once I get through the section with the heavy bermuda grass the rest should go much more quickly.
I agree with your comment on weed cloth...I think that would cause more trouble than it would help!
Thanks for the suggestions...I appreciate the time you took to write.