Performance normally isn't affected by a head gasket failure - that does other annoying things like pushing water into the oil or blowing the water out of the system.
Sure there are posts on here about bleeding but essentially put the expansion bottle on top of the engine. Fill from the rad. Then squeeze the top hose to pump water into the engine. Undo the rad cap and let it fill from the expansion bottle (with the cap loose on that to allow water to move). Rinse and repeat. And turn the heater on and let the air out of the valve on that. I'll get Frederick to do a page on that.
But after overheating definitely bleed the system and try again. Those bubbles could well be air left in there after overheating - the thing that causes the water to fall out is boiling and that leaves air in there. And make sure the cooling system is pressurising properly - if there's a leak, perhaps a hose, water pump, radiator cap seal, or expansion bottle seal, the system will boil before it gets to the temperature necessary to turn the fan on. Pressurised cooling systems boil at a higher temperature than unpressurised ones, and the car is set up assuming a pressurised system.
Clean the connectors on the fan and the radiator thermostat. Connect the fan directly to make sure it comes on when it has electricity. Bleed the cooling system. Run the car, take it for a short drive and let it idle - the fan should switch on and off when it's hot before it bubbles.
If that works then wait until the following day. When the engine is completely cold bleed the system again if it needs it. Go for a drive (10km) and leave the car sulking in a corner until the following morning when it's cold again. Undo the expansion bottle cap and if it hisses then there's not the same quantity of stuff in there as there was yesterday and the head gasket needs doing. See above for good advice on that.