I have a bump on the outside of my vagina that normally is filled with puss and I can pop. Tried to drain today and blood came out. What could this be?

Several things. It could be a sebaceous cyst, it could be a skene's gland abscess, and it could be a bartholins cyst or abscess. However, since it hasn't simply gone away, you really need to be seen by your doctor or a gynecologist.
Infected Cyst. Is the bump in your vagina or on the labia? What you describe may be a sebaceous cyst (clogged hair follicle) or an infected bartholin's gland. Either can get infected by the normal bacteria in the area when the opening gets blocked. That causes the infection. The bleeding comes when you have gotten to the base of the gland or from the skin above.
Staph infection. Maybe i don't get it, but a pus filled sore needs immediate medical attention. What are you doing staying away from the doctor? Don't you see the daily news stories of people dying from staph infections?