Somewhere WAY WAY back in the post, I metioned pressure bleeding. That is the only way to do it! It'll get 100% of the air and 99.44% of the old fluid out of the system in a hurry. That old fluid is what will cause 95% of your future problems from the hydraulic side of the brakes.
You can go out and buy a professional power bleeder if you have money to burn, but if you are on a "make do with wha'cha got" budget, you can throw one together from stuff you probably have around the house already.
Basically what you want to do is devise a way to pump air pressure (and not much at that) into the top of the brake fluid reservior. When you open a bleeder, fluid will be forced straight through the pipes leading to the master cylinder, through the master cylinder, through the brake lines and out the bleeder at the wheel cylinder. "Real" pressure bleeders keep adding fluid as you bleed and make this a one man job . . . if you devise one out of aquarium hose, a bike pump and a couple of drier parts, and it just puts air under pressure into the reservior, it's best to use two people. One to keep the pressure on and make sure the reservior doesn't go dry and one to run around opening and closing bleeder screws. Either way, it just takes a couple of minutes to get ALL of the air and almost all of the old fluid out of the system.
When you pump and bleed, it's kind'a like the fluid takes two steps forward and one step back . . . this tends to break up the big air bubbles into lots of tiny ones that are much harder to get pushed along the way and out the bleeder screw. Of course if your kids or wife need exercise . . . :lol: