You didn't say what year you have, but your sig implies an E30. On my 91 318i, the head gasket at the front sprung a leak (out-of-warranty) at 50,000 miles. A few years later, my water pump broke, and besides that I had them change the front seal, so I suspect the profile gasket was changed as part of that process. Under the intake manifold is a plastic pipe with coolant hose and engine block connections. That's your next possibility and that's the least painful from a money point of view. The coolant should leave some telltale trail when it's dried or drying up (splashguard had the evidence my radiator was finally losing it -- that I replaced myself).
Good luck tracking it down and getting it repaired.