I'm unaware of any current research of type 3 Bile Acid Diarrhoea (BAD)/Bile Acid Malabsorption (BAM) in relation to coeliac disease. There is an increased prevalence of Primary biliary cholangitis, which is also an autoimmune disease, in coeliac disease patients. In Primary biliary cholangitis, bile ducts in the liver are damaged causing problems with bile build-up in the liver. There are genetic risk factors that are shared between coeliac disease and Primary biliary cholangitis, but it is unclear what the direct link between the two diseases is.