Green’s Dictionary of Slang

a.d. n.1

[used on dance cards to disguise a preference for alcohol over dancing; partners’ names were also abbreviated]

(UK society) a drink.

[UK]J. Ware Passing Eng. of the Victorian Era 1/1: A. D. (Ball-room programme). A Drink, disguised [...] The ingeniousness of this arrangement is that young ladies see ‘A. D.’ , and assume the youth engaged.