Hi kdel. I read your question to M2M about your daughter. Hope you don't mind if I respond.
I was VERY shy as a child. So softspoken people couldn't hear me. I was a good student, but hated being called on. I froze to think people were looking at me. People telling me to "not be shy", speak up, be friendlier, smile, none of that helped. It just made me retreat further.
So as you know, nagging doesn't help. Are you an extrovert? My husband is one. He thinks my daughter and I can become extroverts by just wanting it to happen. It doesn't work that way. As I've become older, I care less what people think and my self-esteem has improved over the years, so I do come out of my shell more. But my basic nature is toward being an introvert.
My older daughter is just like me. One way I've tried to help her is by telling her I understand what it's like to be nervous about talking to people, but that good manners and being polite are very important. I practice with her on meeting people - if she meets an adult to hold out her hand, respond to whatever they ask and look them in the eye. It is difficult, but practicing helps. The last time we were at a favorite restaurant of mine, I introduced her to the owner's mother and several employees and she did very well. I could see the pride in her face afterwards that she faced her fears for the moment. Halloween, though passed now, is another great opportunity to practice. Tell her what to say, including looking at the person and saying thank you, and have her practice it out loud with you several times.
Practice for the upcoming holidays. They can be shy even around loved ones, or relatives they don't see much. Teach her how to shake hands, respond. It's tough, but you'll empower her.
What else? Try this exercise. Be somewhat dramatic. We've done this in girl scouts when girls meet one another. Have her greet you, say hi or whatever. Your response should be a mumbled hello, looking down at the floor. Have her do it again, this time looking at her, smiling brightly and saying hello back in a friendly way. Ask her which response SHE liked better. It made her feel better to be responded to so nicely. Tell her when she responds to people like that, it lets them know she is interested in them and makes them feel good.
I'm sure there are more specific ideas, exercises, and books out there on this.
I'm not advocating nagging, pushing, or trying to change your daughter's basic personality. Just gently try to equip her to face life and people.
I hope this helps.