I think you should let her take the lead in her social life and not push her. Facilitate what she needs, but don't push.

I'm an introvert and I find it exhausting to be around people. I have fun going out but I can't do it too much and it makes me tired. Same that I'm perfectly pleasant, can fit in well, but there's only been a few people I've met in my life who I don't need to "recover" from with alone time, even if I like them.

ETA : Rose's post is just right. It's more likely to make your daughter think you think something is wrong with her if you keep bringing it up.