I have known this song for a long time, but only in Russian. About 10 years ago, someone on rec.music.folk told me it was an Odessa cabaret song from the 1920s. I have never heard it in Yiddish or in English. The Russian words have more of a satirical cast:
^^
Noch' nadvigayetsa,
Fonar' shatayetsa,
Svet prolivayetsa
V nochnuyu tmu.
Ya, neumytaya,
Tryap'em prikritaya,
I vsya razbitaya,
Edva brozhu.

Kupite bublichki,
Goryachi bublichki,
Gonite rublichki
Syuda skorey,
I v noch' nenastnuyu
Menya neschastnuyu,
Torgovku chastnuyu,
Ty pozhaley.

Otets moy pyanitsa,
Sam etim chvanitsa,
On k grobu tyanetsa,
No vsyozhe p'yot.
Sestra gulyashchaya
I mat' propashchaya
Da ya kuryashchaya,
Glyadite -- vot!

Kupite bublichki...

Translation, probably wrong in spots -- I don't actually speak Russian:

Night comes on, the streetlamp swings, light slips thru the gloom of night. I, unwashed, clad in rags, and all beat up, can scarcely get around.

Buy bagels, hot bagels, give money, here, quick, and in the vile night, take pity on unlucky me and my private trade.

My father is a drunkard, he boasts of it himself, he has one foot in the grave, but he keeps drinking. My sister is a streetwalker, my mother is a fallen woman, and I am a female smoker, look -- like this!

Presumably, at that point she takes a wicked drag on her cigar.