I bleed the brakes on my 360 from the top using a vacuum pump.

My procedure:

The fill hole at the top of the reservoir has an 1/8 inch NPT thread.
Normally a NPT plug with a small hole goes there.

Take out the plug and put in an NPT-to-hose-nipple, and connect
a vacuum pump via tygon tubing.

In my plane the brake plumbing inside the cockpit is "nylaflow" tubing which is
translucent, so you can see bubbles vs red brake fluid.

Turn on the pump, and watch the bubbles grow to about 100 times their original size.

Most of the greatly expanded air makes it to the reservoir, bubbles up
and ends up passing into the pump.

With vacuum applied the calipers open about 1/4 inch.

Since the motion of the bubbles eventually stops
(1 min) you know there is no leak in the system.  After the bubbles
stop moving disconnect the hose from the nipple and let air back in.
You can watch the few remaining bubbles shrink.
Pump the peddles to push the calipers back into position.

Repeated this process maybe 5 times.   

Top up the fluid level in the reservoir at the end.

Process takes maybe 15 min. Not a drop of fluid on the floor.

You don't need a fancy pump, any that is adequate for vacuum bagging will work for bleeding.

My pedals are very firm now.
--
Jeff Peterson
N273CK L360