It was always my understanding that the word "bume" in "The Bume" referred to the copious smoke billowing from GHB's pipe. E.g. the verb "to bume" meaning "to give off copious amounts of smoke." Unfortunately (?) the word is not to be found (I believe) in the full edition of the Oxford English Dictionary.
Tony Boys
John Dawlings has this to add...
Just found the link to GHB and reference
to the Bume. I thought Bume came from the sequence of nicknames Bailey,
Bummer Bailey, Bummer, Bume.
Possible. I do not now recall where I heard the pipe story.
The change in vowel from "bum" to "bume" might be explained by someone
writing "bummer" as "bumer" which then might have been shortened to "bume"
and caught on as the favourite and permanent nickname that we all love
and cherish. (Tony)