It can be anywhere from a few hours to a few weeks (i.e. the delays on delivering the new 2010's for what was rumored to be EPA clearance). The timing is more to do with the availability of transport than what happens at the prep center.

Your CA can tell if your X5 is actually still "at the prep center" or really just "waiting on transport" and when the transport is expected. BUT this status is the last point at which your CA has info. via the BMW dealer's tracking system. Once the X5 is 'on the truck' your CA is out of the loop until it arrives at the dealer.

Funf Dreisig