I don't in fact shout "brav-"anything. It's not my style. But hypothetically, I can see two ways to look at it.
(1) "Bravo" as a word adopted into the English language, which therefore remains uninflected under all circumstances. (This is how I generally handle Italian musical terms in musical life: "tempos" not tempi, etc.)
(2) If one prefers to maintain the distinction of the endings, then my point of view would be that I am indeed applauding the singer, thanking them for work that I enjoyed. (The singing is already over, but the singer is standing there before me.) With this would go bravo, brava, bravi, according to circumstances.
As I suggested, I go with (1). Being too ostentatiously foreign seems pretentious to me (admitting that this is a matter of taste). I feel the same way about pointedly pronouncing foreign names "authentically" (over-rolled R's, French vowels, all the stuff that Richard Wilbur called "nasal and uvular agonies") in the middle of an English sentence.
[This message has been edited by Jon (edited 11-24-2009).]