WARNING: This page is about a different car, the 2003 BMW 540i, 2002 BMW 540i, and 2001 BMW 540i. However, it is still accessible from the selected car via links, so may be relevant.
Fig 1: Starter System Wiring Diagram (Automatic Transmission)
Courtesy of BMW OF NORTH AMERICA, INC.
Fig 2: Starter System Wiring Diagram (Manual Transmission)