While there are many thing that can cause this, since it only shows symptoms at start-up a likely cause is the fuel pump/module, either taking too long to get up to pressure, or a leaky check valve that allows the system to depressurize too much while sitting.

The "only while sitting a long time" typically points to a bad check valve -- unfortunately the check valve is normally built-in as part of the fuel pump assembly and requires a fuel pump replacement.

Now, to put it in perspective, that has only been my experience with non-BMWs, but most fuel systems work on similar principles.