Once you are done with that bleeding, close the rad cap and shut off the engine, - fill the expansion tank higher than the full mark. The rest of the air will expel as bubbles and the system will suck in coolant from the tank.
You can also get a cap and chop its pressure head off - or stick a U shaped clip in your cap's vacuum valve and install on radiator, this cap will never let the system raise pressure but it will allow air to move to the expansion tank and bubble out - the displaced air will be replaced with coolant liquid from the tank. (mazda/nissan service procedure)
Once you let it run, and then cooled off - remove the clip from the cap and install the cap back - if the whole unit is air tight the level in radiator should be full, fill up expansion tank to max/full line and pack the job up.