Bleeding gums are a sign of active gum disease called gingivitis (inflammation of the gums / gingiva), and is caused by the build up of dental plaque along the gum line and in-between the teeth. The dental plaque contains acids, enzymes and toxins that irritate the gums and initiates an inflammatory reaction. Part of this reaction is for the gums to become very hyperaemic, meaning more blood flow to the gum area trying to combat the irritation. The result is puffy, red and friable gum tissue that bleeds on touching.
Holding back on brushing and flossing is only going to make matters worse, so it is very important that one keeps brushing and flossing throughout, even though the gums may be bleeding a lot. In time, as the gums begin to heal (as the irritant -dental plaque, is effectively removed), they will become less and less inflamed and will return to health where no bleeding will occur on brushing.
Ask your Dentist or Oral Hygienist if your brushing and flossing technique is correct and if you have not already, consider switching to an electric brush, which is twice as effective as brushing with a manual brush.