I had a similar issue after I replaced the radiator that had a hole in the fins.
I thought it was the expansion tank but it turned out to be the transmission thermostat that connects to the bottom of the expansion tank. It's made of plastic, like most BMW parts, and the housing that held the spring in place on the thermostat failed. So the spring was pushing against the bottom of the expansion tank and creating a space for coolant to leak out. I was at a little over 100k miles when this occurred. So check out under there and see if the coolant is leaking there.
Generally if the expansion tank is leaking you can see the white coolant residue on the sides of the tank leaking at the lip on the top part of the tank. Mine didn't have that but I replaced it anyway to avoid the pain later on.