If a master has an internal leak that causes soft pedal, then there should be no air bubbles. Mine had a long-term seep in the rear yet still worked fine until the seal between the pistons failed and there was no pedal at all. If I depressed the pedal fluid would be displaced from the one chamber to the other, not forced into the brake lines.

You should not try to pump up the brakes. Either the pedal gives resistance, or not. And since you had no trouble with your master until you began to bleed lines, I would follow John's suggestion and slowly, gently, bleed it with hoses from the just-cracked bleeder valves back to the chambers. Don't bury the pedal as brake fluid will become airborne, it takes only a little movement each stroke to properly bleed the master. You should feel the pedal return when you are successful, and no bubbles should appear in the reservoir. At that point, close the bleeders, remove the hoses, fill the chambers, reattach the brake lines and start the bleeding process again using the vacuum bleeder, one wheel at a time.