Disclaimer: I'm hella new at this, so take my opinion with a grain of salt.
Shooting from the hip, I think you have every right not to meet her, but only if he gets that. Being that you don't think your voice is being heard, you and the bf need to talk again, because there is a hitch somewhere in your communication together. Assuming you told him that you like the V the way that it is, I think he has to respect your wishes.
From his perspective, I would imagine that he's happy with her and wants to share that with you. Its only natural for him to want the two loves in his life to be friends, especially if she wants to meet you too! It almost seems rude to deny meeting someone that enthusiastically wants to get to know you, so you'll need to reassert that it is nothing against her personally, just that you're not comfortable with that (and may never be).
I'm guessing that having the PDA shoved in your face is different in a V than in a triad, especially since you're mono and she is poly and is probably more comfortable with it. Ultimately I would talk with the bf again and ask him to please cancel the meeting and respect your boundaries. You may be okay with it in the future, but for right now you feel blindsided, especially after having expressed your wishes.
By the way: flawless screenname.