You can use a vacuum pump, no problem. My way is without a vacuum pump. I have used my way for gobs of years. The biggest mistake people do is leaving the front tires on the ground when initially bleeding.
Also, I left something out. When tires are in the air and you have turned stop to stop, SLOWLY, and topped off. Then start the engine and continue the stop to stop with engine at idle. Again, turn slowly and smoothly and continuously. Do not turn 1/8th turn and stop and then 1/8th turn again. Turn all the way, stop to stop, smoothly. Then on ground and repeat and top off as needed and then road test. It may still need a top off because it takes a while to get air out.
Any fluid fill, at any time in the process, should be done slowly.