When was your last dental checkup?
Theres two likely possibilities that I can think of from your description. You either have gum disease (such as gingivitis) and its causing your gums to bleed. If that's the case, then you need to go see a dentist for a cleaning, etc to help the gums heal.
If you don't have gum disease, its most likely trauma from your aggressive brushing causing damage to the gums. Brush the gums gently for a few days and the bleeding should stop as the trauma has been reduced.