I'm a little confused...bleeding the coolant system implies you are trying to get the air out of it...this happens while it is running in the coolant resevior. I think you are trying to flush the system right? If so one of the easiest ways to do this is getting one of those Prestone flush kits. You cut into the heater hose and put their connector in. You can then backwards flush the entire cooling system (heater core too) with water, it really cleans it up well. Then when you drain the radiator and start filling the system, you leave the connector open and fill until the coolant mix displaces the water out of the connector. Real nice way to clean/refill you cooling system. And if you don't like the connector left on your system, you can always replace that section of heater hose for $5.