It's easier and faster opening the bleeder. Open the bleeder when you go to fill the system and close bleeder when a stream of coolant flows out of it. Then do the run engine until thermostat opens procedure.
I did a coolant drain & fill on the wife's 2004 Accord with a 2.4L about a year ago when I first bought the car. I don't recall there being a bleeder on it at all.
I dumped the antifreeze from the pan into a couple of empty milk jugs- mostly to measure how much came out. So when I refilled with Honda Type II, I made sure that that same amount went back in. I was able to pour most of it right into the radiator. Had to over-fill the overflow bottle a little to get the rest in there. It was down to the correct level after a couple of heat cycles.