OP here. Thanks for the replies!
I think several of you hit the nail on the head with the "more the merrier" mentality. She definitely has that, and I do not. Plus, Jen is a very good friend of Beth's, so I know in her mind it was "Yay! Now I get to see the movie with TWO friends!" whereas now I'm thinking, "Now I'm seeing the movie with one friend and one stranger." But I think I would have felt the same if she'd invited someone I did know well. It really made me feel like just my company was not good enough for her.
And I was really pretty clear about this being a special outing for us. We were having trouble determining which screening to go to, because she was supposed to be at work during one, and I was supposed to be at work during the other, and we were both having trouble finding someone to cover us (I eventually got my shift covered). But at one point she said that maybe we wouldn't be able to see the movie together after all and I said "No way! We have to go see it together! It won't be any fun if I don't see it with you!" (That's copied word-for-word from a Gchat.) So while I realize that is not an explicit "... so don't invite anyone else, mmmkay?" I was upfront about the fact that seeing the movie was only part of the appeal, seeing it with HER was the point.
And I 100% agree with those that say the text message was a bad idea. I can't even call it hindsight, because I remember thinking as I was sending it that it was a bad idea! I don't have a good excuse for not following that instinct, except that, as I mentioned, I had never confronted her before and was not especially looking forward to doing it then. I also think/thought having further discussion in Gchat was a terrible idea as well, but at the time I couldn't figure out a way to say "I would rather discuss this in person" that didn't come across as very dramatic.
My original post was about three times the length (heh) so I edited out a bunch of details. But since people asked, about a week after making the plans with Beth, I found (in my couch!) a gift card for the movie theater, so I told her I would use it to buy the tickets. She did protest, but I thought it was perfect, because we were getting to do something geeky, and do it for free! I sincerely didn't look at it as paying for her ticket, and told her as much, because it was essentially found money - I didn't buy the gift card in the first place, and apparently hadn't missed it when it fell into the couch. She agreed, but said she would compensate by buying the snacks at the theater, which she did end up doing.
And she really did keep saying "stupid" which is what I thought was so over the top. Maybe not that I
was stupid, per se, but the idea that she would have to ask me before inviting someone was stupid. She also kept saying that absolutely NO ONE else she knew would have minded that she did this. And much later I had the thought that if I hadn't said anything, she would have assumed I was ok with it too. So a more likely scenario is that she does have other friends that might be bothered by this, but they're smart enough to know she would not take well to the confrontation and let it be. Smarter than me, clearly!