Gosh she sounds exactly like our daughter. She can be soooo shy and yet once you get to know her she is very clever and funny. She has always been very mature compared to her peers.
She had her own "lunch bunch" at school but they did not go out together very often, maybe once or twice a year. They were involved in a variety of activities so it made it hard to get together.. They were also very much into their grades, so they spent lots of time talking about school work.. Only a few of them were boy crazy, so they were not into all of that type of thing.. They are not big consumers and found shopping boring! (I have been in retail for over 35 yrs, love to shop).
I was the PTA President and very involved in her schools so I would encourage the girls to help with the different projects that the teachers administrators and others needed help with. This way even if they did not want to go to the dance, this was a way to at least get them involved by making and then setting up the decorations. The school Carnival they loved but instead of just hanging out, they volunteered to be the photographers.
All of us moms of these girls encouraged the girls to get together. We would host game nights for them, providing the food. Or movie nights.. One family is really into Sci Fi so they would host all day viewing parties.. This was maybe 4 times a year. I wish it had been more.
In High School it did not change much, but our daughter found a few more friends and was involved in community service art etc.. so those kids become their own community.. Now that our daughter is far away in college, she has blossomed, she literally glows when she is on campus.
. She has found others that are like her with the same interest, think being smart is important. Since they all live in dorms, they all care for each other.. These other girls are now her best friends and like sisters to her.
So just encourage your daughter to try to organize some activities with these friends every once in a while.. Meeting for a movie, meeting at the book store, bowling, game night.. Or you moms could organize it. Once the girls get there they have a great time, they are just not always confident to put themselves out there..