@Manteo
Thanks everyone, I feel like I've tried all the suggestions though. Saying hello myself, telling her she can wave instead, asking her why. She says she's scared, I ask what she's scared of and I get a shrug.
Can you imagine what she might be scared of? Making some suggestions to her in a way that shows you have compassion for her, might help her in the longer term. Asking her what she is scared of can come across as really dismissive and disheartening to a shy little person tbh. She needs to hear that you understand her or are at least trying to. If you don't understand her, you might want to take some time to imagine what it's like to be her tbh.
These social graces are really quite a far way away for many children who are on the quieter side. What they need first is to build a foundation of language to be able to communicate how they feel (scared, anxious, etc.) to trusted loved ones, which only happens if they feel their loved ones are hearing them. Then a few years of practice of naming their emotions to themselves. Then a few years after that of creating personal and social habits to cope with those emotions... it's a long road, it's not something that you just solve one day by forcing her to wave at people or whatever. That's not how it works, not if you want her to develop authentic, confident social skills.
The first step will always be to create a dialogue with her over a long period of time. Not trying to "solve" her emotions, just listening to them and acknowledging them. If you do that for the next few months, you might gain enough insight into her social habits to start asking her how she might like to change, and what her ideas are for how to change. Ultimately her social interactions are her own choice, you're just the one who acts as the good example, and as her sounding board.