I syphathize with the OP: as a DM I do not want players who don't really want to be there.
The concept and explanation of D&D don't make many people very enthusiasitc to start off with, but she wants to give it a try. The worst that can happen is that SHE is predisposed to thinking it's dumb, in which case nothing will disabuse her of the notion, and the DM should pick up on it pretty quick (is she sighing a lot when asked what she does? does she appear apathetic about her character's fate?), and let her linger in the background like she wants to do. She's not giving it a fair chance in that situation, nothing will force her to do so, so let her think she's passing judgement and continue to have fun anyway.
Though that's the pessimistic approach. I'm pretty used to introducing new folks to the game, and enthusiasm is contagious. Tell her you're excited to have her along and assure her that even if she sucks, you won't hate her.
Even let her know that she needs to be ready to think it's awesome, because no one can convince her of something she doesn't want to believe.
If she wants to give it a try (and REALLY give it a try), the worst thing you can to is assume she doesn't REALLY want to give it a try and so let her sit in the back not having any fun while the boys run around and kill goblins.
And even if she's largely undecided, seeing how much everyone else is into it might sway her.
*shrug* I guess I wouldn't assume she doesn't really want to be there given, y'know, that she says she does.