I've heard spraying with roundup immediately after cutting the coastal pasture will knock out the bahia and not hurt the coastal. I've never been brave enough to try it myself. I have had some luck with Cimmaron (generic ally).
I was under the impression that glyphosate (roundup) indiscriminately killed everything.
I heard that applying a certain fertilizer formulation (dependant upon a soil test) would suppress the bahia and encourage the bermuda. If anyone can find this study please let me know.
Glyphosate (Round-up, Eraser, etc) is indiscriminate, BUT it takes 5 qts. / acre to kill bermuda. THe producers who are using glyphosate are applying 1 pt. (1/10 the rate to kill bermuda) right after a hay harvest.
Ally or Cimmarron (DuPont's new name for it) works well at 3/10 oz per acre when the bahia is actively growing. You may have to trat two years in a row as there is enough seed to come back for several years.