Can you tell me how I could stop my gums from bleeding when I dental floss?

Normally not. Healthy gum tissue should not bleed when flossing. From time to time, you may irritate the tissue or have some localized areas that need attention, but if you have generalized bleeding, see your dentist. Bleeding can also be increased with meds, taking too much aspirin, ill-fitting fillings and crowns, etc.
Gingivitis. Bleeding gums while flossing can be a sign that you are at risk for, or already have, gum disease. The bacteria and other particles, constantly form a sticky, colorless toxic “plaque” on teeth causing the gums to become inflamed and to easily bleed. This is a serious problem, which should be checked by a dentist. The good news is that this condition is curable. Call your dentist today!
More info needed.. When was your last dental checkup and cleaning? If more than six months ago, it's time to make an appointment. Dental care is more than just a mouthful of toothpaste. If you are being seen regularly by your dentist, you may be traumatizing your gums. Have the hygienist show you how to floss correctly.