Interestingly, "Mudder Dinah" is the first song in Bullen's book, "Sister Susan" is the second-- and it too is decribed as seldom being used on ships. The note to the song says that "The circumstances under which Mr. Bullen first heard this tune are described in 'Log of s Sea Waif'."

And you are in luck, "Log of a Sea Waif" can be downloaded here: http://www.archive.org/details/logofseawaifbein00bulluoft

Download the .pdf version, and go to page 34 of the .pdf-- the song, complete with the melody, is there!

Like "Mudder Dinah," Bullen explains that he learned the song in Guyana.

I commend "Log of a Sea Waif" itself to you, it is an interesting read.