I found a recording of this on a CD called Bing Crosby and His Hollywood Guests - one of the guests is Bogart, who says he learned the song as a child. The African Queen came out in 1951. I can't identify the woman who sings a verse or two on the recording - maybe Lauren Bacall? Can anybody find this in print earlier than 1951?

Alan Mills recorded this in 1954 on a Folkways album called More Songs to Grow On. The song comes from a sonbook titled More Songs to Grow On by Beatrice Landeck (1954, Edward B. Marks Music Corporation), pp.116-117. The songbook gives no source information. Here are the lyrics of the Mills version:

THE BOLD FISHERMAN

There was a bold fisherman who sailed out from Pimbeco
To slay the wild codfish and bold mackerel.
When he arrived off Pimbeco, the stormy winds did wildly blow.
His little boat went wibble wobble and over board went he.

CHORUS
"Twink-i-doodle-dum Twink-i-doodle-dum,"
'Twas the highly interesting song he sung.
"Twink-i-doodle-dum, Twink-i-doodle-dum"
Sang the bold fisherman.

He wriggled and scriggled in the waters so briny-o.
He yellowed and bellowed for help, but in vain.
Then downward he did gently glide to the bottom of the silv'ry tide;
But previously to this he cried, "Fare thee well, Mary Jane!"
CHORUS