Check to see if is your overflow tank where you put the anti-freeze in. I have worked on tons of those bmw's. I ran a mechanical shop for many years too. The parts are not that expensive. Those years were very comomn for overheating and leaking and happened on the 5 series and 7 series.
First let it sit running and look for leaks. Make sure it does not overheat.
Normally if you are using a lot of coolant and it has no leaks, then it is internal headgasket and the exhaust will smoke white. I am sure it is just an external leak and is common.