This date is uncertain by a single day at most.  Caryll uses Lady Mary to defend Hortensia on Saturday May 6 ["Your Dulcinea … has ne'er a glance for you o' Saturday!", Chapter IX], his exposure of Rotherby at White's was "three or four days later" [Chapter IX], and the duel was at "seven o'clock next morning" [Chapter XI].  I've chosen May 10 over May 11 solely because the former is my birthday.