This girl(lets call her "Lucy") is one of my best friends.However, she shows off so much, its unreal. We both dance and are on the school dance team, so when we're with our friends at lunch or break, she'll just randomly start doing the dance routines.She also just randomly breaks into her ballet routine anywhere&everywhere and it's quite embarrassing and annoying, as people stare at us. 
one of our friends(lets call her "Megan")has invited us to her house for next week.I can't go, but Lucy can. When her and my other friend were discussing what they should do over text, Lucy told Megan to ask me what they should do.Meghan said 'but abbie isnt going' and lucy said 'ask her anyway!' I think she wants to rub it in that I'm not going and she thinks she can do it the best if they're doing something I would enjoy.
Oh, and one last thing.We all get the train to school every morning and she's very loud and obnoxious on the train, as she speaks all of our personal business(boyfriends etc. etc.) at the top of her voice, so other pupils and the public can hear. She also brags loudly about 'always getting distinctions in her ballet exams' and how she can do cartweels,handstands and a back-walkover.

I'm sick to death of her show-offy ways but i don't want to fall out with her, as she can be quite mean to people she doesn't like... what should I do?

---

I think you should break off with her slowly, like staying 10 feet away from her or shortening your responses to her. And try to get a new friend who is NOT a show off like her. Then maybe she'll get the idea that you don't want to be friends with her anymore. 

Another way is to just talk it over, but this may backfire. Good luck!

---