There is the correct way to bleed brakes, then there's a better way
Start by making sure all the bleed nipples open. Nothing more depressing than getting ready to do the job and have a rusted nipple break off. Ideally remove each nipple and coat the threads with anti seize.
Take out as much fluid from the master cylinder as possible (turkey basters work well) Clean out as much crud from the bottom and then fill it to the top with new fluid.
Beginning with the wheel farthest away from the master cylinder. Get a piece of clear plastic pipe that will fit over the nipple and put the other end in a jam jar. Now have a friend ready to open the nipple.
Pump hell out of the brake pedal 5 or 6 times then hold it down as hard as you can. Get your friend to open the nipple. When the pedal is on the floor have your friend close the nipple. Repeat this until clear fluid starts coming out of the pipe, top up the master cylinder and then move onto the next wheel.
This will accomplish 2 things. It will stir up all the crud lurking in the bottom of the master cylinder and it will force out, at a good pressure, all the crud and all the air bubbles clinging to the inside of the brake lines.