There are two "tech" ways to bleed, as well as the hand-pumped, conventional method.
Tech one is use a large volume syringe and inject the fresh fluid from the bottom and allow it to flow out the master res in a controlled manner. This drives the air and oil contaminates up the system to bleed it. Air likes to move this direction. Back in the day, this method was the KTM recommended service procedure for mineral oil based Magura clutches. Dunno what they suggest for Brembo Dot3/4 clutches...
Tech two is to use a vacuum bleeder and suck the new fluid down the system and out the bleeder nipple, using vacuum force. Very easy to do this way with a H/F $19 hand pumped vacuum bleeder.
edit to add:
Then there is the baby oil vs Magura blood vs 2.5w fork oil debate: which to use and get the smoothest and most consistent feel