I think I would lead by example. You know -- just try never to be embarrassed or feel awkward about the fact that she's not saying 'hi' back. Don't discourage her from holding your hand when you first arrive somewhere new. Accept her completely just the way she is.
But at the same time, smile and laugh and talk cheerfully to people around her so that she can see how mama does it. And when they say 'hi' to her, and she just hides her face or something, don't react yourself the way a shy person would react ...don't be embarrassed or push her to respond. Just laugh cheerfully with the person, and say, "Oh, they never perform, do they? Haha!" And just act like everything's fine and keep smiling. Let her see your example.
Seems like that would bring the two important parts together -- the security of knowing it's all OK, no matter what she does or doesn't do -- and the inspiration to be more sociable someday like mama. That's what I would do.