Quite true, always best to do the pumping method. There is only one other better way, but it is costly in fluid, really difficult sounding and I have never done it, reverse bleeding, where you start feeding fluid from the ends you normally drain from.
As for your bubbles... when did they do this? I experienced a master cylinder going out once when there were bubbles coming out of the line connection. This was on the clutch master cylinder and was at the brass fitting's O-Ring....

91 Jeep Wrangler YJ, carpet, tires, trailer hitch. yea....