Bermudagrass makes an excellent turfgrass. However, its excellent ground-covering ability also makes it a pest in flower and vegetable beds.
The herbicides fluazifop (Grass B Gon) (click for sources) and sethoxydim (Bonide Grass Killer) (click for sources) can be used in some cases but not all ornamentals are tolerant of these chemicals.
Fenoxaprop Bayer Advanced Bermudagrass Control) (click for sources) is labeled for use in ornamental beds.
Read the label to be sure.
In my case, I use a piece of cardboard to shield my flowers as I spray glyphosate (Roundup, etc) onto the bermudagrass. I examine my flowerbeds every few weeks in summer and re-treat as necessary.
If a flowerbed is next to a bermudagrass lawn, consider installing a six inch wide “no grass” border of bark chips or brick pavers between the two areas. Spray or pull any grass that tries to invade the bed across the narrow strip.