Bleeding on the outside of your teeth won't cause them to stain, but gums really shouldn't be bleeding when you floss. It could mean you have gum disease. If you haven't seen a dentist for awhile, it would be a good idea to get a check up (including gum exam) and cleaning.
First, your gums should not bleed when you floss. This is a sign of a chronic bacterial infection that, if left untreated, may lead to permanent damage to your gums, bones and teeth. The blood could result in surface stains of your teeth and it could result in stain around leaky fillings or crowns.