The hardest part about situations like this is saying what needs to be said, and I know I have a heck of a time with it, even when I know that I have every right to say it. This is how I would plan to go about it, but I know from experience I don't always manage to execute my plan.
I would open the conversation by asking for clarification if she were planning on taking the class or not (something like, "Mary, I'm confused, are you taking the Quilting for Beginners class next month? I'm trying to get a headcount.").
If she said yes, then I would remind her of the fee and class supplies needed (or whatever you would do for any student taking the class). If she said no, then I would say, I'm sorry, but only people taking the class can attend.
I would try to leave it at that rather than give too many reasons, because determined people have a way of countering every reason. ("It's a distraction to have non-students there." "Oh, I won't be a distraction!") ("I try to limit the classes to six people." "So if the class isn't full, I can attend!"). But since sometimes it's unavoidable, the reasons I would focus on are the need to keep the class small and the need to have a strict policy on this to keep people from taking advantage.
Realize that her friend may want to drop the class if she's not going to be there.
You can't say this to her, but having her there will actually probably prevent her friend from meeting new people in the class.