The expression “to put the bite on one” means: To mooch, cadge, shake down, or, more plainly, to beg.
This American slang seems to have developed from the entirely innocent token of fondness, “to bite one’s ear.”
In Romeo and Juliet, Mercutio makes reply to a quip from Romeo, his dearest friend, “I will bite thee by the eare for that iest.”
The expression, though perhaps not the action, originated from the French, mordre l’oreille, a soft caress and whispered endearment accompanied by a gentle nip of the ear.
Now, in making a request for a loan or in begging, one does not shout from the housetops, but if possible one whispers his wants in the ear of the intended victim.
He is “putting the bite on,” though from appearances he is but “biting a friend by the ear.”