Well, she had to do *something* to keep her parents from finding out she's a lesbian. They are *very* conservative.
Growing a beard sounds like a strange way to hide the fact that you are a lesbian.
I'm going to assume this is not sarcastic and thus explain the joke : beard can mean something else.
I had a conversation about this how this term has been misused. It makes sense as the context of concealing infidelity. You have a mistress and a wife, and you can't have this unattached mistress hanging around at social events. So you hire some guy (a beard) to pose as her beau. By all rights, he should have a beard.
It doesn't make sense with mixing genders because, well, women don't have beards. So the only context that it really applies to in regards to concealing sexual identity are:
1) You're a straight man, but you need a husband to give the pretense of being gay (your beard), and/or a male companion for your female companion (the beard for her)
2) You're a gay woman, but you need to give the pretense of being straight, so you need a male companion (beard) for you and/or your female companion.
So now that I've explained it, Teproc's explanation does make sense in this context, since we're talking of lesbians, though the link he provided provides a broader context (defining a beard as a man or woman) with which I disagree.
More explanation:
http://en.wikipedia.org/wiki/Beard_(companion). (They include both definitions without mention of this controversy.)
