I have a 2002 bugeye wagon and just replaced the radiator with a Koyo with no cap. I figured with one less cap there was less to break or leak. Plus thats how the car came. I had no problem getting air out of the system. First I ordered the Lisle 24610 spill free funnel. Amazon has it for $21. You can read about it in the cooling system FAQ thread.
There's a small vent hose that goes from the top of the radiator on the passenger side to the expansion tank. I disconnected it at the expansion tank and tied it to the hood prop so it was high enough coolant wouldn't flow out. Next I capped the expansion tank connection for this hose to keep coolant from flowing out while filling the system.
Using the spill-free funnel I then filled the system. Almost all the air trapped in the radiator went out the vent line tied to my hood prop. This eliminates the need to burp the upper radiator hose but go ahead and try it to make sure. I did.
Next I reconnected the vent hose from the radiator back to the expansion tank. If you skip this step you'll have a fountain when you turn on the engine. Ask me how I know.
I then started the engine and let it run until the top of the radiator was hot and the driver side cooling fan came on. I made sure the funnel had coolant in it. I had some bubbles but not many.
Next I shut the engine off and replaced the expansion tank cap and filled the overflow tank to the upper line. The few remaining bubbles worked themselves out the next time I drove it and were replaced with coolant from the overflow tank.
There is no need to turn on your heater since there are no heater valves in the cooling system. You need to be sure you put the thermostat in correctly if you replaced it. There's a small jiggle pin in the thermostat flange, it has to be at the top. It vents air out of your lower radiator hose when filling.
On Subarus with two caps, one on the expansion tank and one on the radiator, the lower pressure rated cap, 108 Kpa and with ears, goes on the expansion tank. The higher pressure one, 137 Kpa with no ears, goes on the radiator. The expansion tank is the highest point in the cooling system. This will make sure any air bubbles in your system will be vented out through the expansion tank cap. Having the caps reversed will means pressure increase when the engine warms up will vent coolant out instead of bubbles.