As a motor mechanic for 38 years and having bled hundreds of brake systems, the only surefire way to achieve it is to gravity bleed. First, I syringe all the old fluid out of the master cylinder reservoir then top up the reservoir with new brake fluid. The next step is to get four clear plastic hoses to attach to bleed nipples at each brake caliper or slave cylinder with a container at each hose to catch the old fluid.
Open each bleed nipple onehalf to one full turn until clean fluid with no air flows through the clear hoses, it will only take a couple of minutes, then close the bleed nipples. Just make sure the reservoir is always topped up! Gravity has just done all the hard work for you! The air bubbles flow out with the clean brake fluid or disappear out the top of the master cylinder. It also works for ABS systems.
Iíve never had a problem with air in the system after bleeding this way and only my reliable self is required.
ED: Iím going to have to give this one a try. It sounds fiendishly simple. Most of the staff here have some Heath Robinson technique that involves broom sticks, string, pulleys and swearing to bleed their brakes yet seem curiously resistant to change!