I always recommend the various vacuum bleeder systems, I use a Mityvac but there are others available. See for example https://www.amazon.co.uk/Mityvac-MV8020-Automotive-Bleeding-Silverline/dp/B005O2LQLQ/ref=sr_1_3?ie=UTF8&qid=1490189717&sr=8-3&keywords=mityvac+mv8000
There are various versions available, plastic or metal, with/without gauge (not needed for brake bleeding but can be useful for other tasks). If you bleed bike brakes more than once you'll appreciate the outlay.
The key is that you can achieve a continuous flow of fluid which will purge air much more