More on Blue Billy from Infoplease:

• Blue Billy - Blue Billy (A). A blue neckcloth with white spots, worn by William Mace. More likely the allusion ...
• Billy - Billy A policeman's staff, which is a little bill or billet. A pocket-handkerchief. “A ...
• Dictionary of Phrase and Fable: B - Definitions, origins, and illustrative excerpts for words, phases, and literary allusions starting with "B"