This starts to answer some questions why exercise may incresae bile flow.
Circulation in the liver is greatly aided by the action of the abdominal muscles and the diaphragm, the thick musculature that divides the chest from the abdomen and expands the chest cavity. As the diaphragm expands the chest, it compresses the abdominal cavity. The liver sits just under the rib cage and is attached to the diaphragm with ligaments. With every breath, the liver is gently compressed, aiding the circulation of all the fluids through it. This movement is essential to the liver circulation, the production and movement of bile into the gall bladder, and for the circulation of lymph. This can account for some of the well-known health benefits of aerobic exercise or of deep yogic breathing.
From an article by Paul Bergner