I'm new to BMW's, but that sounds to me like a fuel pressure problem or water vapor in the fuel system.
Pressure in the fuel line declines overnight, when you first start the car in the morning the electric fuel pump doesn't have time to get the pressure where it should be. On the second time the pump has enough time to put the proper amount of pressure in the system.
I'd check for pinhole leaks in the fuel line, and failing that I'd test the fuel pump.