Here's the version from Folksinger's Wordbook (Page 183); also in the pink (Vol 1-6) Collected Reprints from Sing Out!, page 13. (almost the same as those in the Digital Tradition):

ROUND THE BAY OF MEXICO

Then 'round the Bay of Mexico
Way, Oh, Susianna,
Mexico is the place that I belong in,
Round the Bay of Mexico.

Those Nassau girls they love me so,
'Cause I don't say everything that I know.

When I was a young man, in my prime,
I loved those young gals two at a time.

Nassau gals ain't got no comb,
Comb their hair with a whipper backbone.

Goodbye gals of Nassau town,
I'm bound away for the fishing ground.

New lyrics by Paul Campbell (The Weavers)
Music Adaptation by Tom Geraci
TRO Copyright 1953 Folkways Music Publishers

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The earliesk known version of the song is almost the same. It was collected in Nassau in 1935 by Alan Lomax and Mary Elizabeth Barnicle from the singing of Henry Lunday and a man known only as "Pappie."

ROUND THE BAY OF MEXICO

Then 'round the Bay of Mexico
Way, Oh, Susianna,
Mexico is the place that I belong in,
Round the Bay of Mexico.

Oh, why those yellow girls they love me so?
'Cause I don't say everything that I know.

When I was a young man, in my prime,
I loved those young gals two at a time.

Those Nassau gals ain't got no comb,
They comb their hair with a whipper (grouper??) backbone.