Just found your post so I shall sort you all out!
Closest is Lloyd: yes, DBH-B was issued by Buckinghamshire C.C. in August/September 1964. It was followed (not by EBH, but) by DKX-B in September.
Yes Luton is in Bedfordshire, and yes it did issue XD (and XE) registrations in the 10-year period 1964-1974.
John "jukebox": BH was issued by Luton only between 1974 and 2001.
Andrew "master brummie": no, not August 64 to July 65. The first four letters A,B,C,D were issued January to December (1963-66). The "August to July" period started with F (1967/68).
Anything you would like to know about the number plates of this period is in my book Motor Vehicle Registration Numbers of Great Britain 1963-1974 (always available from David Thomas Motoring Books). There is a sequel 1974-2001, too!
Otherwise, you're welcome to ask me any questions you like. And please see the Youtube video which I did with "geoffbuyscars" - I hope you will find that it is a hoot!
all best wishes
Jonathan