I don't really know how they work; I had thought that the bitterness stimulated release of bile. I just decided to try them again after someone at the health store suggested them as an alternative to enzymes. I think Flamengo's answer makes sense.
I just know that my digestion is so much better now. The brand that I like the best is NatureWorks Swedish Bitters (because it has bergamot and reminds me of Earl Grey tea), but I think that any bitter substance will work.
I would give it a few weeks rather than expecting something immediate...