I do know that I have a continuous drip into my duodenum, but the liver is stimulated to produce bile during a meal to refill the reservoir. In my case the reservoir is absent so the bile has to be produced "on demand". Normally the bile produced by the liver during a meal would be stored in the gallbladder for the "next" meal. This is why I have to watch my fat intake so as not to overwhelm my system with undigested fats.

"The amount of bile produced by the liver during the ingestion of fats, is much greater than what's produced between meals. "The flow of bile is lowest during fasting, and a majority of that is diverted into the gallbladder for concentration. When chyme from an ingested meal enters the small intestine, acid and partially digested fats and proteins stimulate secretion of cholecystokinin and secretin. As discussed previously, these enteric hormones have important effects on pancreatic exocrine secretion. They are both also important for secretion and flow of bile"

So it's established that most bile production in the liver occurs during meals and slows down between meals.

So, because the Liver Flush call for about 12 hours of fasting, and an additional 18 hours prior to that of light, low fat eating, bile production should be minimal during this period. Once the 4 ozs of olive oil is ingested, the liver starts trying to produce bile at a high rate. So with or without a gall bladder, the rate of production is the same.

Another intersting medical tidbit of information;

"Fats. Although fats (particularly saturated fats found in meats, butter, and other animal products) have been associated with gallstone attacks, some studies have found a lower risk for Gallstones in people who consume foods containing monounsaturated fats (found in olive and canola oils) or omega-3 fatty acids (found in canola, flaxseed, and fish oil). Fish oil may be particularly beneficial in patients with high triglyceride levels, because it improves the emptying actions of the gallbladder."

More from the medical world:

"Cholesterol is Needed for Bile Production

The first thing to realize if you have no gall bladder is that you need cholesterol to produce bile which assists with the digestion of regular long chain fats and oils. Note that short or medium chain triglycerides like coconut or palm oil do not require bile for digestion.

Cholesterol is required for the production of bile and the very foods that have sufficient and healthy quantities of cholesterol are those that are, you guessed it, quite fatty, like liver, egg yolks, cream, and butter.

Avoiding fat is potentially going to compound problems with digesting fat in the long run as you won’t be getting the healthy, unprocessed cholesterol you need to produce bile!"