Rich it's been so long since I've looked at an M44, but I'm pretty sure that hose goes to the secondary air pump check valve. There's some good pics in this thread:
http://www.318ti.org/forum/showthread.php?t=9431 The hose looks like item#13 and attaches to item#15 (shut off valve) in this illustration:
http://www.realoem.com/bmw/showparts...58&hg=11&fg=45 Edit; Nope, I'm wrong. Not sure what attaches to that fitting.