Green’s Dictionary of Slang

(a) constr. with the, money (usu. owed from gambling); esp. in the phr. a bit of the old.

1890		Sporting Times 3 May 1/4: It was a deuce of a bother to find anyone who would cash a crossed stumer without deducting some of the old, old, very old.
1903		A. Binstead Pitcher in Paradise 155: The slender off chance of falling across a stray defaulter and raking in ‘a bit of the old’.
1962		R. Cook Crust on its Uppers 28: We had a good bit owing down to the old.