I tried the "pump from the bottom with an oil can" bit and made huge
mess.
Couldn't seem to get the fluid to pass through the cylinders.
It did however leak at the bleeder. puddles. profanity.

So, I tried a new (to me) approach. My Lancair
has a reservoir shared by the right and left sides.

It has two cylinders each side, in series.

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

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

The brake plumbing inside the cockpit is "nylaflow" tubing which is
translucent, so I could
see bubbles vs red brake fluid.

I turned on the pump, and watched the bubbles grow 100 times.
The brake fluid does not expand or boil.

Most of the greatly expanded air made it to the reservoir, bubbled up
and went into the pump.

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

Since the motion of the bubbles eventually stopped
(1 min) I know there was no leak in the system. After the bubble
stopped moving I let air back in,
watched the few remaining bubbles shrink, and
pumped the peddles to push the calipers back into position.

Repeated this process maybe 5 times. Pedals very firm now. Not a
drop of fluid on the floor.
Topped up the reservoir at the end. Process takes maybe 15 min.

I think I will now try the same trick on the landing gear hydraulic
system.

-Jeff