E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Kiss the Mistress (To).
To make a good hit, to shoot right into the eye of the target. In bowls, what we now call the Jack used to be called the mistress, and when one ball just touches another it is said to kiss it. To kiss the Mistress or Jack is to graze another bowl with your own.
Rub on, and kiss the mistress.Shakespeare. Troilus and Cressida, iii. 2.