As O says above, a 'nabob' was a rich man - particularly one who gained his wealth in India - based on the fact that the word was a version of 'nawab', the title for a Governor in India. Bookies, of course, are always thought to be wealthy, as we see in claims such as "You never see a bookie on a bike."
The Prix du Nabob was the name of a major horse-race in France in the late 19th century which could be another possible connection.
I wonder, though, whether there may be an element of 'naybob' in there...ie someone who refuses (says nay)...as bookies are notoriously reluctant to accept some bets.
There might even be a joke on the notion of 'neighbob', given the horse-connection!