'Bunburyist?'—the explanation is withheld until he confesses why he's Ernest in town and Jack in the country. Which identity hides the truth?

JACK. Bunburyist? What on earth do you mean by a Bunburyist?

ALGERNON. I’ll reveal to you the meaning of that incomparable expression as soon as you are kind enough to inform me why you are Ernest in town and Jack in the country.