This is the version I learned as a kid, maybe from a Dinah Shore or Andrews Sisters recording, or something like that. Mitch Miller, maybe?
Is the version in the DT a bawdy parody of this - or is this a cleaned-up parody of a traditional song?
-Joe Offer-

BELL BOTTOM TROUSERS
(words and music by Moe Jaffee)

Once there was a little girl who lived next to me,
And she loved a sailor boy, he was only three.
Now he's on a battleship in his sailor suit
He's a great big sailor man, but he's just as cute:

CHORUS:
Bell Bottom Trousers, coat of navy blue,
She loves her sailor, and he loves her, too.
When they're together, he thrills her thro' and thro'
With his Bell Bottom Trousers, coat of navy blue.


When they walk along the street anyone can see,
They are, oh, so much in love, happy as can be.
Hand in hand they stroll along they don't give a hoot,
He won't let go of her hand even to salute:
CHORUS


Copyright 1943, by Chappell & Co.