I have a pretty simple method for bleeding the cooling system.

If you have a mityvac or something to pull vacuum and a radiator cap with a steam purge, this will work really good:

-fill radiator and resovior (or use a jug of coolant for a resovior)
-attach your mityvac to the steam vent tube with a brake fluid "bleeder" resovior in line (cap-off wherever the other side of your steam vent goes to, ie. upper rad. hose)
-pull vacuum (hand pump only gets about 5psi), then hold the steam release open on the radiator cap, and watch it suck up coolant from the resovior, continue until constant fluid is constant without bubbles
-disconnect vacuum pump and reconnect steam vent line as quick as possible...

Big air pockets on a dry motor can sometimes take over 2 gallons of coolant

Jack the font of the car up high, turn on the heater, and fill the radiator when the car is at operating temp. This is how it is done on Mercedes diesels as well.

That is how I have always done it

This is the easiest way to fill any coolant system I work on Porsches and this is the only way to evacuate all the air out of the systems. It worked great on my car as well.
RADKITPLUSA, Vacuum/Filler, Cooling System

There are several others that Snap On makes, but this is the one that I like.