Well the reason it's over heatig may not be because of bleeding it. These engines, although very well built have an aluminum alloy head that doesn't like heat very much. It's very possible that you blew your headgasket. As I previously mentioned check your oil. When coolant and oil mix it turns milky brown. It's quiet noticeable.
A headgasket itself is $75. It's the labour involved that makes it expensive. Most places will har the head sent out to be inspected for cracks and machined if nessecary. it's DIY-able but you need to rent the BMW camshaft tool.