Here's a write-up I did a while ago for another forum - thought you guys might find it useful
This method works on the principle that air bubbles rise in a fluid – so you are working with gravity (rather than against it) to eject any air through the reservoir. The bleed nipple on the caliper is usually the lowest entry point in the brake line system, so this is the point where the fluid is introduced.
1. Go to the local chemist and buy a 20cc syringe. Tell them it’s not for drugs. These are about $1-2 each (the syringes, not the drugs).
2. Get yourself some clear hose – the same stuff you probably have used for normal brake bleeding duties. Cut a piece that’s about 10-15cm long and push this on the end of the syringe. Now you are ready.
3. Open the reservoir cap and suck out the old fluid (if any) with the syringe and tube. Discard this fluid.
4. Place a suitable ring spanner on the caliper bleed nipple (normally 10mm). Make sure it has enough "swing" room to open and close the nipple (about one third of a turn).
5. Fill the syringe about 3 quarters full with fresh fluid (straight from a new bottle). then hold the syringe upright and draw some air into it, clearing the tube of fluid.
6. Push the tube over the bleed nipple. Facing the syringe down, open the nipple slightly and draw a SMALL amount of fluid out of the caliper with the syringe. This will fill the tube with fluid and allow any air to rise to the top of the syringe. Don’t draw too much or you will suck air into the master cylinder.
7. With the caliper nipple still open, push the fresh fluid from the syringe into the caliper. Be careful not to push any of the air from the syringe back into the caliper. When this is done, close the nipple and remove the tube (a good tip here is to close the nipple and draw the syringe – creating a suction effect in the tube over the nipple. Remove the hose and any remaining fluid will be sucked back into the syringe. Nice and tidy).
8. Repeat the process from step 5. Keep an eye on the reservoir level – if it approaches full, use the syringe to remove the fluid as per step 3 (if you’re stingy enough, you might re-use this fluid for your next attempt at step 5).
9. If you have twin calipers, move to the other caliper and start the process again from step 5.
You can also use the syringe to draw fluid out of the caliper. This is handy when you are bleeding the system from dry, as there will be air in the caliper above the brake line entry point that you won’t be able to push back up the line.
With a bit of practice, you will find that this method is the quickest way to bleed a brake system – and you will use minimal brake fluids in the process.