Is there an aftermarket USB->DockConnector cable that works with an iPhone 4 + bumper case?
Maybe this'll work: http://cablejive.com/istubz

EDIT:
Whoops, maybe not. The 1st party cables are a precision molded plastic that is thinner than the 3rd-party clones as detailed in this video @ 3:40 - 

http://youtube.com/watch?v=XpmLvY2XNPg