"...Bilirubin levels can be used to identify liver damage/disease or to monitor the progression of jaundice. Increased total or unconjugated (indirect) bilirubin may be a result of hemolytic, sickle cell or pernicious anemias or a transfusion reaction. If conjugated(direct) bilirubin is elevated, there may be some kind of blockage of the liver or bile ducts, hepatitis, trauma to the liver, cirrhosis, a drug reaction, or long-term alcohol abuse...."
From: http://www.labtestsonline.org/understanding/analytes/bilirubin/test.html
Gilbert's Syndrome is also a possibility when you have a normal direct bilirubin and an elevated indirect bilirubin. Gilbert's is a genetic disorder in which indirect bilirubin is elevated. It is considered to be a benign disorder and not a threat to the health of the patient.
In my opinion the bottom line is that an elevated direct bilirubin suggests a liver or bile duct disorder whereas an elevated indirect bilirubin suggests a non-liver issue.
Good luck,
Mike