Alice? Wot means "salivated" in your original posting of Bad Girl? Here is one from American Memory. It had no title, so I have added "Lena."

LENA

Among the myriads of Gotham's fickle flappers,
Saucy in manner and in feminist ruses schooled,
Pursued each night by would-be trappers
To elude their profane grasp, and leave 'em fooled
Is little Lena Caffuzzi from Fordham
Who, seeing a man, runs toward him.

Yes, Lena she loves to lure 'em and leave 'em
All trembling with anger and passion intense;
She gets a huge thrill when she thus does deceive 'em
Notwithstanding there's one she'll someday incense
To the point where he'll grab her, and woe betide her!
She'll find, soon enough, a stirring inside her.

Then poor little Lena, lamenting her tricks
Will find herself caught in one heck of a fix,
And may her poor mother persuade to believe
That she was immaculate when she did so conceive.
But Mom will tell Pop, an excitable Wop,
Upon whom this version wil be a sad flop.

No, indeed, not her father, will the story mislead.
He'll know, for he's wise, that some beau did the deed,
And with a gun, and a knife, and a loud cry of rage,
He'll start out at once on a bloody rampage.
The while, the sad beau, discretely may soar
On a plane that will take him to a far distant shore.

So at last we see Lena in a squalid dark flat,
Alone, all alone, with her loud squalling brat.
While its daddy, still free with the boys "over there",
Has forgotten long since the maiden fair,
Poor, foolish, young Lena, who out for a lark,
Was pursued and subdued in New York's Central Park.

Supposedly written as a warning, by the brother-in-law of Mrs. Rose Ivanoff, about 1926. I found it by going to American Memory and typing in Bad Girl's Lament.