This is Kitt. Bile reflux, which occurs when bile — a digestive fluid produced in the liver — flows upward from your small intestine into your stomach and esophagus.
Unlike acid reflux, bile reflux usually can't be completely controlled by changes in diet or lifestyle. Instead, bile reflux is most often managed with medications or, in severe cases, with surgery.
Ursodiol is one prescription medication for bile reflux treatment. Anti-reflux surgery may be necessary in some patients. Fundoplication, typically used to treat acid reflux, is one of the surgeries that is used for Bile reflux.
Bile reflux often accompanies acid reflux, therefore, you may want to look at the same lifestyle changes recommended for people with acid reflux. Reference: Mayo Clinic on Digestive Health, Second Edition
Take care and I hope this has helped.