I perform a "reverse-bleed" on my motorcycles, but I have done this on cars and trucks too.
I most-often use a 60 cc syringe and a 3 inch length of 1/4" I.D. clear plastic tubing. I ise either a worm-drive or a spring-steel hose clamp on one end of the plastic hose, and the other end is fastened to the 60 cc syringe. Get the "irrigation syringe," not the "luer-lock" syringe which is meant to accept the metal hub of a hypodermic needle. The "irrigation syringe" has a tapered end which easily-accepts a length of small-diameter tubing.
Use the syringe to empty the old fluid out of the master cyl. Then flush the syringe clean, and fill it with brake fluid. Place the end of the tubing onto the brake bleeder ****** so it is tight using the clamp. Open the bleeder valve, abd slowly push the plunger, flowing the clean fluid into the bleeder, the caliper, and towards the master cyl. Keep doing this until you see clear fluid in the master cyl. At first, since you will be purging the old fluid from the line, what is in the master cyl should be dirty. You may need to empty the master cyl of this dirty fluid. When your fluid starts to be clear coming into the master cyl, close the bleeder and go to the next bleeder. Repeat this at each ****** until your fluid emerging into the master cyl is totally-clear. At this point, check all the bleeders are snug, and, with the travel you normally-have. Clean up any spilled brake fluid. Refill the master cyl to the full level. Replace the master cyl cover. Press the brake pedal (or fan the brake or clutch lever on a bike) repeatedly to pump it. You should very quickly have a firm pedal, now try-out your brakes.
I use this for the brakes on my 1,000 cc sportbike, including the clutch, which is hydraulic. I've been doing this method for years, I have 3 different Mityvacs I've used since about 1982. But this is the method I've used almost exclusively for the last twenty-plus years.
One word about doing this on bikes: the master cyl whether for brakes or for hydraulic clutch, has two holes in the floor. The one closest to the lever/handlebar end is large, the one closest to the banjo bolt for the hydraulic hose is tiny. The tiny hole has to be open and unplugged for your brakes or clutch to work properly. Dirty brake fluid and its contaminants can plug the small hole. If you have-to, use a small pin to clean any debris from the hole. When you are pushing the syringe plunger, the small hole should flow a stream of fluid out of it. If you encounter resistance to being able to flow fluid from the syringe, the small master cyl hole is probably plugged. Be aware that there may be pressure built up in the line, and using a small pin to clear it may launch fluid a foot or more into the air! Wear safety glasses, and protect your painted surfaces.
If the line you're trying to bleed has air in it, you will see bubbles erupting from that small hole. As the air is purged the bubbles will decrease in volume and size, and may become small, 'fizzy' bubbles, and they should stop altogether when you have purged all the air. After that, you should have a solid stream of fluid like a small geyser coming from the tiny master cyl hole. That means you're done, on the circuit for the bike. If you were to squeeze the brake or clutch lever on your bike now, a column of brake fluid would erupt from that tiny hole, possibly landing outside the master cyl. Time to fill the reservoir and replace the master cyl cap! Do that, and fan the lever rapidly a few times and you should quickly feel the resistance and lever travel you would expect. Check that everything is tight, and give it a road test.
My bikes do not have ABS.
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