Is that something she’s directly told you or your guess as to her motivations? As someone who in adulthood discovered they were neurodivergent, I grew up thinking I was “shy” because that’s what everyone told me. Turns out it was autism with ADHD. My point is just because someone is behaving like they’re shy, doesn’t mean there isn’t something else going on.

As for coping mechanisms, school will be a challenge for her soon, right? Might be helpful to factor that into whatever you ask of her - if she’s already stressed/tired from dealing with social situations in school, extra activities may be too much. Also, if she has friends who she does these activities with outside of class, maybe invite one of them to the class with her so she has the anchor of someone she knows?

But most importantly, don’t try and shape her into who you think she should be. She may be shy her whole life and that’s fine. Everyone doesn’t need to be an extrovert.

It sounds like you’re trying to “make” her not shy instead of talking to her about what she’s feeling and giving her coping mechanisms to deal with that. Exposure therapy type approaches don’t really work for something like that. She’ll be less shy when she’s more comfortable, so I’d suggest working it from that angle instead.