When using dental floss, remember always to keep pressure on the floss so that it is against the sides of your teeth and not pressing against the gum. Flossing is a way to clean the teeth and get rid of plaque. If you put pressure on the floss and allow it to press on your gums, you will be causing injury to your gums.
Usually in the beginning it is quite normal for some bleeding to take place. However, if it occurs continuously and your gums are always bleeding after flossing, then you are not using the correct technique to floss your teeth. However, do not stop flossing just because bleeding occurs. Instead get in touch with your dentist and ask him or her to show you the correct way of using dental floss.