Do I have gum disease?

possible.
Of course, you may just be trying to brush your teeth. If you are taking blood-thinning drugs or supplements, such as warfarin (coumarin), aspirin, or coenzyme Q10, your gums will also bleed. In spite of this, bleeding gums usually means that you do not get rid of all plaque on the gum line where the gums come in contact with the gums. The best way is to use dental floss regularly in addition to brushing your teeth.