If you get air in the system on a specific caliper, make sure you have enough brake fluid in the reservoir, then ask a friend to help.
Bleeder closed, ask the friend to pump the brakes 5-6 times (until it's hard) and hold the pedal pressed while you open the bleeder - air will come out along with brake fluid, and the pedal will go to the floor; close bleeder and ask friend to start pumping the brakes again.
Repeat until all the air is out / brake pedal stays hard from the first/second press.

Only after the air is out, you can do the gravity bleed method.

Source: I got air in my front right caliper, wanted to get the piston out but I forgot the bleeder was open and pumped the pedal once.

 

This is why I love my Speed Bleeders. I have no doubt that the gravity method works great if you follow the directions fully, but I have pretty strong faith in check valves. I just bled mine today to get some once-boiled fluid out of the calipers; one of them burped a little air. Much better pedal feel now.

 

when having someone help you bleed brakes. dont have them pump the pedal before holding down, it will only take longer this way. what happens is you break up and disperse the air in the system. making more air bubbles usually. instead - crack the bleeder, have them put medium pressure down on pedal till it gets to the floor and then close bleeder. no pumping needed.