Same car, Same Problem
Do not despair! I picked up my 2013 X3 28i last week. The car was born on 12/6/12. Perfect drive to dinner, approximately 130 miles from dealer and on the way back to NYC. Stopped for dinner and then while backing out of the parking spot I noticed a heavy stream of washer fluid pumping onto the rear window. Next I heard a high pitched whine coming from the passenger side of the engine compartment directly in front of the glove box. I couldn't stop as I was now on the approach to the G.W.B in N.J.
Upon arriving home I added a gallon of windshield washer fluid (was getting the low fluid message). The fluid pumped out almost immediately and the whine subsided after the car "went to sleep." The dealer replaced the washer pump and control module...got the car back yesterday. All is great! 3 cheers for our BMW dealer. Kudos to BMW as well. I drove home in yesterday's blizzard....the car was perfect.