Years since I saw the play, Dr Bill, but I seem to remember that the plot hangs on the inability of a young man to talk coherently to young ladies of his own class, whilst being perfectly at home in talking to lower-class females - particularly ladies of the streets and barmaids. The "Classy Lady" who is setting out to marry him pretends to be such a low character in order to woo him (rather, to enable him to woo her!) - therefore, I guess, the meaning of "stoop" in this instance is, "to lower oneself"

(But not in the sense of a female bending down to gather the fruit of the horse-chectnut!)