Personally, I rarely fields complaints that concern bacopa - except in some urban amenity/community ponds where virtually any vegetation is considered taboo (unsightly and/or snake-magnets).
I've also never treated bacopa, but suspect that it would respond to glyphosate, imazapyr or 2,4-D; if deemed necessary. A good surfactant must accompany any topically applied herbicides.
@Brian: the sparce amount of leaf-structure (herbicide entry-points) on the photographed specimens may be partially to blame for your lack-luster treatment responses. Imazapyr+MSO surfactant would be my first choice for treating bacopa, assuming irrigation-restrictions don't pose an issue.

Kelly Duffie
Cypress, TX