The DC power outlet would definitely have less noise on it while the engine is not running so you should see less interference (or the possibility of interference) when the engine is off. You could try the black cable plugged into the iPod and the A/V connections for the screen but leave the USB part unplugged (disconnected) from the power adapter and see if you still get interference issues (with and without the engine running). It is possible that the apple cable (the white one) is of better quality (has better shielding) than the black one. I assume the black one is a cheaper aftermarket version?!?
If the black cable works without interference even when the engine is running but disconnected from the power adapter, you may need an isolated type power adapter. I assume that the one you currently use is most likely just a buck converter style regulator (meaning it is non-isolated).
2009 750i individual | Citrin Black Metallic | Platinum Merino Extended Leather | BMW Individual Composition Package (includes Sport Package) | Dynamic Handling Package | Multimedia Package | Technology Package | Executive Package