Sounds like dried coolant which has a chalky white appearance. Hard to tell without seeing it where it might be coming from, given that with the fan running and car going down the road the air inside the engine compartment is swirling all over the place.
Common leak points that might be hitting the fan are temperature sensor in lower hose, radiator, expansion tank and what might be the most likely, the vent tube.
The vent tube a thin tube that runs from the top of the radiator on the drives side (US), under the metal shroud that covers the radiator and fan, over to the coolant tank. Its job is to provide a pathway for excess coolant to flow out the top of the radiator and into the expansion tank. It is constructed of two short preformed rubber tubes clamped to a long piece of extruded plastic tube. Therein lies the problem as this plastic tube grows brittle with age and heat and can develop hairline cracks which can be difficult to find. And often if left untouched it seems to stay together, but when moved or handled during other repairs you can often kiss it goodbye.
Hopefully some of the $2200 you have spent was to install a new water pump, thermostat, coolant reservoir expansion tank, belts, hoses and the vent tube. Any 545i on the road, regardless of miles, is old enough that preventive maintenance on the cooling system is critical.
What you have spent so far will seem like a drop in the bucket if your all-aluminum engine is badly overheated due to a coolant system failure.