E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Biddy (i.e. Bridget).
A generic name for an Irish servant-maid, as Mike is for an Irish labourer. These generic names are very common: for example, Tom Tug, a waterman; Jack Pudding, a buffoon; Cousin Jonathan, an American of the United States; Cousin Michel, a German; John Bull, an Englishman; Moll and Betty, English female servants of the lower order; John Chinaman, a Chinese; Colin Tompon, a Swiss; Nic Frog, a Dutchman; Mossoo, a Frenchman: and many others.
In Arbuthnots John Bull Nic Frog is certainly a Dutchman; and Frogs are called Dutch Nightingales. The French sometimes serve Liège frogs at table as a great delicacy, and this has caused the word to be transferred to the French; but, properly, Nic Frog is a Dutchman.