In the notes to Superbia et Odium, his translation of Pride and Prejudice, Tom Cotton writes,
Latin has neither appropriate nouns nor convenient abbreviations (Mr, Mrs, etc) by which to indicate social status; to avoid the cumbersome repetition of Honestior, Matrona where Jane Austen has used the English abbreviations, I have devised the forms Hr and Mra. Elsewhere, I have adopted Hera, Domina, and Senior (Miss, Lady, Sir) to usages which are not strictly classical, but in which the meaning is unambiguous.
As I mentioned in a comment above, Terence Tunberg, who along with Milena Minkova runs the University of Kentucky Institute for Latin Studies, which (as far as I understand) uses Latin as its main language of spoken and written communication, uses Dominus for "Mr." and abbreviates it Dno. in the dative. If I learn more case abbreviations I'll update this answer.