The way we train doctors in the U.S., only those that have internal medicine or gastroenterology type training end up knowing very much about viral hepatitis. Your doctor's advice not to worry about it is not good advice.
You'll be fine dating, but not ignoring hep b & c. Hepatitis C is a terrible disease that can lead you all the way to liver failure with no symptoms whatsoever. Please go see a more specialized doctor like a gastroenterologist or better yet, a hepatologist (a gastroenterologist further specialized in liver disease). Only they can tell you if you are one of the lucky few who really has nothing to worry about. Since you have antibodies to both B & C, your case is worse, as you may be getting liver damage from both diseases. Please go sooner rather than later.