I have episodes of heartburn, usually from eating beef or potatoes and I find it very soothing to drink a splash of bitters in club soda. I make homemade bitters with ginger, grapefruit, gentian root, and several spices that seem to be the most effective. Bitter herbal liqueurs are popular in Europe for before or after a meal to stimulate the appetite or aid digestion.
Gentian root is one of the most common bitter agents. While I don't know of any clinical studies, gentian root has been used in herbal medicine for centuries to treat digestive issues. It makes sense from an evolutionary perspective because bitter compounds are mostly found in plants and are often more or less poisonous. If the body produces more digestive enzymes in response to bitter flavors, the extra enzymes can neutralize the poison or extract more nutrition from the plant material. It's certainly not totally effective, salivary enzymes won't save you from hemlock poisoning, but it could reduce the ill effects of mild poisons.