You don't have to empty the master cylinders completely and I suggest you don't pump all the fluid out.
I went to a medical supply place and bought myself the largest syringe they had and some taigon tubing suitable to fit onto the bleeder screws. Clamp the tubing onto the syringe. Warm it up to stretch it if you have to. Speed Bleeder sent me some nice stretchy silicone type tubing when I bought bleeders there once that works well for this. I've since put my OEM bleeders back on though since I changed my bleeding method. You need lots of rags or paper towels no matter how you do this and I cover all areas of the bike below the masters with lots of rags just in case of a drip. They happen...
Once everything is together suck up the new fluid up into the syringe and tubing, then hold the rig upside down and push all the air out. Don't worry about air in the syringe. It will rise up when you pump it in.
Attach the tube carefully as you can to not allow any air in to the bleed screw and open the bleeder. Pump the fluid in. You will have to do this several times while removing any old fluid from your master reservoir as you go.
Replacing the brake fluid from the bottom up instead of pumping it down with the master was the only way I could totally bleed the air out of my system after installing new lines. It works so well that I will do annual brake fluid replacement that way from now on.
Way easier to push bubbles up rather than down. I think I was doodling during the physics class that explained why air rises so easily in liquids.