(First, the standard disclaimer--I am not a lawyer, and none of what follows is to be construed as anything even remotely resembling legal advice. It is merely the educated opinion of a magician who happens to make part of his living as a sound designer for theatre [in other words, it's my job to know this stuff :) ].)
That's not entirely correct, Pete. If the use of the music is considered to be a dramatic usage, licensing falls under the individual music publishers, and NOT ASCAP and/or BMI. Pre-show/post-show music, and possibly even bump music while choosing an audience volunteer would fall under an ASCAP/BMI license; music used as an integral part of the production, contributing to the dramatic content of the performance, would generally fall under the rights of the publishers.
It's kind of a weird division as to what the publishers/licensing organizations consider dramatic usage vs. non-dramatic usage; you'd be well advised to do a bit of research before assuming that an ASCAP/BMI license covers you.
Furthermore, when an ASCAP/BMI license does cover you, typically the venue will have a blanket license that covers all events in the venue, and it isn't your responsibility (although it is possible that you could be named in a suit if an appropriate license isn't in place).