One word: Mityvac.
You can't open the bleed nipple and then pump the brake pedal several times. Each time the pedal comes back up, it will suck air back into the bleed nipple. You should press and hold down the brake pedal, open the nipple, allow the fluid (and air bubbles) to come out, then close the nipple
before you release the brake pedal. Then repeat until the new brake fluid reaches the bleed nipple. That's why it's a 2-person job, or 1-person, easy peasy, with a Mityvac
.
Don't forget to keep the brake fluid reservoir topped up, or you will suck air into the top of the system.