I've bled a few K's as well. Tbh I've never really had the problems (airlocks etc) I see written about here though. I do wonder if there are other faults in the cooling system when these problems happen.
Usually I'd flush well, and with the heater on full, I just fill up through the expansion tank with the coolant rail bleed screw removed and pop the screw back in when the coolant reaches that level, then continue to fill to the max level and replace the cap. Run, for a bit, top up if necessary, then keep an eye on the level for a few weeks, topping up again if required.