Is it possible to have serious gum disease but have no bleeding?

Generally no but yes: The short answer is no and long one is yes! In general gum disease presents with inflammation and irrigation which leads to bleeding. However late stages of gum disease can leave you with damaged gums that do not bleed and doesn't give any more signs of until teeth feel loose.

Yes: Gingivitis means swollen gums that bleed by brushing. Periodontitis is more advanced gum disease and there is bone loss associated with it. Loss of bone around the teeth might not be associated with the bleeding gum while brushing. A dentist by examining and measuring can tell if periodontal disease exists.

It's possible: You've assumed that bleeding is a sign but that isn't always the case. Smokers have little if any bleeding (constricted blood vessels), giving them the false sense of security that their gums are healthy. Usually they are not.