I had a gymnast for a while who was so incredibly shy when I first started coaching her. She would only talk if you asked her a specific question and if you asked a yes or no question, you would usually get a head nod instead of a verbal answer. She was very nervous about messing up and would get bright red if she did something in front of the whole group. One of the big things that I tried to do for her was trying to giver her "compliment sandwiches" ex: Sally that one was definitely better than the last. Try to make sure you are trying to keep your legs together. I really liked that connection though! Another thing was really trying to challenge her little by little rather than giving her big pushes (after she had learned her round-off back handspring by herself, I continued to stand close to her when she did them so that she could feel confident in her abilities)
As she progressed through our program, she finally got moved to an invite only level in our rec program so it was a similar group of kids every session. This was a huge thing and after a little while she was talking a little bit. She still wasn't a big chatterbox but she wasn't painfully shy anymore. She would even ask me for spot or help before I got the chance to ask. Unfortunately, she decided to be done with gymnastics so she could focus on sports she could do in high school (they live in a small town and don't have a high school gymnastics program). On the last night she was there, she gave me flowers and a note that her mom had written to me. The letter thanked me for being her coach and helping her grow in the sport, emotionally, and socially and helping her daughter learn to self advocate and all this wonderful stuff.
Really what I am trying to say is that its best to ease her out of her comfort zone little by little. Try to let her get used to things and eventually she will probably start to come out of her shell and be herself.
Hope this helps!
