"Rose of Washington Square," with words by Ballard MacDonald and music by James F. Hanley, appeared in Ziegfeld's Midnight Frolic (1920). The usual singer was Fanny Brice (portrayed by Barbra Streisand in the musical Funny Girl; see "Don't Rain on My Parade" here).

There were standard lyrics and lyrics for a comedy version of the song. A song by this title also appears on the soundtrack of the movie Thoroughly Modern Millie (1967).

http://www.stlyrics.com/lyrics/thoroughlymodernmillie/roseofwashingtonsquare.htm
Singer:
They call me Rose of Washington Square.
I'm withering there, in basement air I'm fading.
Pose in plain or fancy clothes?
They say my turned up nose
It seems to please artistic people.
Foes, I've plenty of those.
With second-hand clothes, and nice long hair!
I've got those Broadway vampires last to the mast.
I've got no future, but oh! What a past.
I'm Rose of Washington Square.

http://www.midnitesun.co.uk/lyrics/lyrics04/wb04p111.txt
ROSE OF WASHINGTON SQUARE
Words - Ballard MacDonald

VERSE
A garden that never knew sunshine,
once sheltered a beautiful rose,
in the shadows it grew, without sunlight or dew,
as a child of the city grows.
A butterfly flew to the garden,
from out of the blue sky above,
the heart of the rose set a flutter,
with a wonderful tale of love.
He told her of birds and of bees,
of the brooks and the meadows and trees, he whisper'd,

CHORUS
Rose of Washington Square, a flower so
fair, should blossom where the sun shines
Rose, for nature did not mean, that you should
blush unseen, but be the queen, of some fair garden
Rose, I'll never depart, but dwell in your
heart, your love to care, I'll bring the
sunbeams from the Heavens to you, and
give you kisses that sparkle with dew, my
Rose of Washington Square.

VERSE
But after the summer comes autumn,
when flowers their petals must close,
for the songbirds are still and the breezes are chill,
to the cheek of the blushing rose.
The gay butterfly's wings are folded,
the heart of the rose has grown cold,
a butterfly lives but a season,
and a rose in a week grows old.
The meadows the brooks and the trees,
like the birds and the flowers and bees, need sunshine,
(Chorus)

----
Comedy Version

VERSE
She's Rosie, the queen of the models,
she used to live up in the Bronx,
but she wander'd from there down to Washington Square,
and Bohemian Honky Tonks.
One day she met Harrison Fisher,
said he, "You're like roses, the stems,
I want you to pose for a picture.
On the cover of 'Jim Jam Jems'".
And that's how she first got her start,
now her life is devoted to art, they call her,

CHORUS
Rose of Washington Square,
she's withering there,
in basement air she's fading,
pose in plain or fancy clothes,
they say her Roman nose,
it seems to please, artistic people Beaux,
she's plenty of those, with secondhand clothes,
and nice long hair, she's got those
Broadway vampires lashed, to the mast,
she's got no future but oh! what a past, she's
Rose of Washington Square

VERSE
She's terrible good as a model,
the artists are stuck on her charms,
once a feller said he would paint Venus from her,
only Venus ain't got no arms.
Rube Goldberg her figure admires,
he dresses her up in a veil,
and uses her shape for the pictures that
he draws in the Ev'ning Mail.
He promised sometime when he's free,
that he'll model a statue of she, they call her,
(Chorus)