Take the caliper loose from the bracket but, keep all the plumbing attached. Pop out the pads. Clean everything in and around the pistons with degreaser, a toothbrush and then soapy water. You want that area meticulously clean.
Now start pumping the brake lever and put your hands in the caliper as you do it. Feel the pistons start to travel out. Keep pumping it until the pistons are extended to where you're afraid they're going to pop out. If they pop out, you went too far. You'll have to gauge this on your own from how deep the pistons feel.
Once the pistons are extended, clean the outsides exposed surfaces of the pistons with the toothbrush and 0000 steel wool and soapy water, followed by plenty of rinse water.
Now as hard as you can, squeeze those pistons back into the caliper with your hands. It shouldn't take more than a firm grip with your fingers. You'll hear the fluid rushing back into the master cylinder. You'll hear bubbles being forced by all the velocity.
Pop the cap on the master cylinder and I promise you'll see bubbles. Let those aerate out and repeat the pump-up and forcing the fluid back process a few more times. That will give you a good, 100% bleed.
It sounds complicated but, it's really not. You're just cleaning the pistons so you're not forcing brake dust and other crap into the caliper seals. Otherwise, it's just pumping the pistons out slowly, then forcing the fluid back uphill, very quickly by compressing the caliper with your hands.
I had to do the same with 1525's clutch upon reassembly. I pumped the fluid downhill, with the piston all the way out against the circlip. Then I tightened the screw quickly by hand, until the piston bottomed. I backed off the screw and repeated. I did that a few times and got a great bleed out of it, without using a Mityvac (couldn't find the Mityvac reservoir and wanted it done that day).
