Well if the smoke goes away while driving...still could be anything. But from the rest of your description, it sounds like your cooling system needs to be rexamined, and you may need to patch up or replace that radiator.
Bleed the radiator again tomorrow morning. Please follow my advise on the bleeding...the first with the engine off, fill to brim, let coolant overflow from the bleed screw, stop when the bubbles run out, repeat the whole procedure after starting the car and it reaches operating temperature. And yes, a pressure test on your radiator is an excellent idea, apologies forgot to mention that earlier. At some point, do carry out a compression test on your engine to rule out problems there too.