Are you sure that when this lady said she would come with her friend, she meant, as a non-paying observer? The other times this happened, did you know ahead of time that the observers were coming? I think, first, you should take some definite steps to eliminate this problem for future classes. Establish an official policy in your mind, and then have it clearly stated in your sign-up materials, your studio and in any other promotional materials you prepare. I'm not sure what the best way is to state what should be obvious: If you don't pay for your seat at the class, you don't attend the class. I think including the idea that 'observers are a distraction' would be good. This might not occur to non-teachers, who may think, the more the merrier. In the future, when someone informs you that they're coming with their friend to class, you will have an answer ready: 'You're welcome to come if you pay for the class, but you already know all the techniques I'll be teaching, and observers tend to be a distraction to me and to the people who are there to learn.' It's best to deal with it when the subject is brought up.
As far as the current situation, you may have to choose between having the class environment you want and insulting/losing your friend/customer. If you tolerate her presence this time, you can preclude it happening again by taking the steps mentioned above. You would avoid a direct confrontation, and though she might suspect, she won't know that the policy change connects specifically to her. If she asks, you could just say that it's been a problem several times, so you had to make an official policy.
If you don't want to deal with your friend attending this class, I think being frank is your best option. Tell her you've been thinking about what she said about coming with her friend, and it's been weighing on your mind because of past experience of people's friends attending class with them, and would she please tell her friend that she won't be able to accompany her because you have a policy that only those paying for the class can attend.