How about signing her up at the Boys & Girls Club, Girl Scouts, or a local teen club? They have other teens there and since they are in smaller groups and doing different activities, she might feel more comfortable. My daughter was also very shy but has surprised me lately by going to her summer camp and picking out the kids who were sitting alone or reading a book and approaching them to talk/ask them what they are reading, and taking it from there, rather than perhaps gravitating towards the popular kids or sitting alone. As a girl who has also been bullied for her weight and height and who would be afraid to even say hi to another unknown kid, it was very encouraging to see that confidence from her. She will talk to kids about anything, from video games (which is why I guess most of her friends are boys), to the newest sci-fi movie, to her favorite song that week, she will even dance or talk to some of the kids who have taken dance and ask them to show her some dance moves.
I don't know if you have this where you live but here, some weekends, some of the parks have nature exploration sessions for kids, so there are kids of all ages and they do things like teach them how to look for birds with binoculars, or kayak tours in groups. Is there anything like that you can sign her up for, where she might meet kids, especially kids who would most likely be introverted? A community center in your neighborhood? Kids in the neighborhood? How about going to a popular teen hangout like an arcade type of place where she can volunteer for games that require 2 players? Drama classes? Dance lessons? Group music lessons?