In my similar situation, both the left and right side sending units had gone bad. My fuel gauge dropped so fast, you could almost see it move going down the highway. The transfer siphon worked fine. Since the fuel pump is part of the right side assembly, it was replaced as part of the service. The job is done by accessing the top of the fuel tank from underneath the rear seat cushion. My replacement was done at 245,000 miles.

2002 X5 3.0 282,200 miles
2004 325i 120,900 miles