Here's a version from Randolph/Legman's Roll Me In Your Arms

BELL BOTTOM TROUSERS

When I was a serving maid, down in Drury Lane,
My master he was kind to me, my mistress was the same.
Along came a sailor boy, as happy as could be,
And he was the cause of all my misery.

Bell-bottom trousers, coat of navy blue
He'll climb the riggin' like his daddy used to do.

He asked for a candle to light him up to bed,
He asked me for a pillow to put beneath his head;
And I, silly lassie, thinking little harm,
Jumped into the sailor's bed to keep the sailor warm.

Early in the morning, about the break of day,
He handed me a five-pound note, and this to me did say:
Take this, darling, for all the harm I've done,
Maybe it'll be a daughter, maybe it'll be a son.

And if it is a daughter, bounce her On your knee,
But if it is a son, send the bastard out to sea.
Bell-bottom trousers, coat of navy blue,
He'll climb the riggin' like his daddy used to do.

Notes:
Text from Mrs. I.C., Springdale, Arkansas, March 27, 1951. She had it from Mr. T.E., Fayetteville, Arkansas. Mr. E. says it is the original of the "Bell-Bottom Trousers" song of World War II, but he learned it in North Carolina, about 1908 (this may be a misremembering, as the text is of the 1920's or 30's type).

The Book of World-Famous Music says this:
while no doubt somewhat older, no printing of this song has been found than in the book Bottoms Up!, edited by Clifford Leach and published July 10, 1933...