Bermudagrass certainly is a tough plant, and difficult to control when it gets out of bounds. It isn't terribly shade tolerant, so anything that provides shade will slow down its spread. However, I'm not aware of any groundcover that would be effective in choking it out. You may be able to install a physical barrier at the edge of your flower bed to keep it from spreading into the bed. However, any barrier will have to extend deep into the soil to prevent it from going under. (Also, watch for rhizomes spreading over the top of the barrier.)
A thick layer of mulch will help keep bermuda grass manageable, but some hand weeding will still be needed.
Another alternative to digging is to use a grass herbicide. Look for a products such as Fusilade, Ornamec, Grass-B-Gon, Sethoxydim, or Acclaim that kill grasses, but do not affect broadleaf plants. (Make certain that your plants are on the product label as being safe to use the herbicide on.)