United States of America.
So far I have found two Dudley's that emmigrated to America. Michael, a descendant of James W.H.Dudley has kindly sent me the information you will find listed below. Gary, another descendant allowed me access to his site where I found information on other Dudleys that feature on this site. Thank you to both of them.
Jesse Dudley b. 18 Dec 1842 Houghton Conquest, Bedfordshire, UK
James White Hinds Dudley b.2 Nov 1844 Bedfordshire, UK