For the next guy who runs into this:
How to bleed the ABS pump manually:
Bleeding Master Cylinder on the car (generalized, not specific to e9x M3)
Gather your supplies.
Jack up the car.
Place a container or jar underneath the master cylinder's bleeder nozzle or the place for the hose attachment.
Ask your helper to slowly pump your brake pedal several times.
Have your helper press and hold down the brake pedal.
Detach the hoses connecting the brakes and the master cylinder.
Examine the brake fluid.
Reattach the hoses to the master cylinder.
Have your helper release the pedal.
Repeat until the air is out of the master cylinder.