If you don't have to wait on a ship at South Hampton and don't get held over at the VPC, 5 weeks from build completion to arrival at the dealers is the fastest you can expect for a West Coast delivery, as illustrated by the timeline for 2002 MCS:
04/26 - On Order (received production number)
05/03 - Status 111 and 112
05/17 - Status 150 (Week 23 [ending 06/07] build)
05/27 - Status 152 (being painted)
05/28 - Status 160 (released for distribution - a week early)
05/29 - Status 182 (waiting for train)
05/30 - Status 193 (in Southampton, loaded on Tricolor)
06/25 - Status 196 (in Oxnard, discharged from Tricolor)
06/26 - At VPC
06/27 - Released to carrier
06/29 - Arrived at dealer (East Bay MINI)