I reverse bleed shimano brakes.
with the bike level and the caliper below the lever, take reservoir cap off.
Use a syringe with a small tube on, attach to bleed nipple.
open bleed nipple and draw all old fluid out with syringe.
take another syringe full of fresh fluid
attach to bleed nipple
open bleed nipple and slowly force fluid back up thru the system until you have filled the reservoir.
Close bleed nipple, put cap back on and job done.
Seems to work for me.