Bacchus is not a Latin word--the "ch" consonant does not exist in native Latin. Bacchus is from Greek Βάκχος, in use certainly by the fifth century if not earlier. LSJ suggests an etymology from *ϝάκχος, which would mean that this title is cognate with Ἴακχος, another of Dionysus' alternate titles. How that relates to ἰάχω, "to shout in revelry," which appears in Homer I couldn't really tell you, since the verb seems to predate the noun (in the written record at least, discounting the mentions of Dionysus in Linear B). But that's what LSJ says. The title of the play is exactly what it says in English and Latin: a Βάκχη is a Bacchante