I know you don't want to say anything harsh to her when she already feels down, but there is one message that got through to me about shyness and low self esteem-which I struggled with for years. I had an acting teacher who didn't allow any negativity in his students and had very strict rules for positive constructive criticism. I learned a lot about life in that class even though I ended up not being interested in acting. He had an especially hard time "breaking out" the really shy people.
He explained that shyness and low self esteem are actually hostility and ungratefulness. Of course everyone protested and the debate ensued, but he had some points.
Basically, it is respectful to your creator, or the world in general to appreciate your gifts by acknowledging them and feeling grateful for them by admitting to yourself you have them. To feel bad about yourself is a choice to discredit your blessings-which many other people wish they had.
As for shyness, people don't know (and arent' always impressed) that you are shy. For all they know, you don't feel THEY are worthy of reaching out to. It is much better to be selfless and deny your own self inflicted insecurity, even though it's difficult, in order to shine and respect other people's time. You may not FEEL like going and smiling at someone and asking how THEY are doing-you may FEEL like moping to yourself and acting shy. But what does the nicer person do? You have the power to overcome these choices, and when you do, your self esteem builds because you are giving to the world instead of denying its blessings.
These concepts really resonated with me, especially realizing it was my choice to feel insecure and scared and shy. Since you know her home life is supportive and she has no reason for this, if you feel she can handle it, you should explain this to her. It's the dark side that tries to keep us down with shyness and low self esteem, and it succeeds with many people-especially when they have been dragged down by family etc.
No, she may not naturally become a social butterfly, but she can improve things a lot by a concerted effort to reach out to others, be friendly and confident and be thankful for what she has, if she only looks at it that way. It's very important so that she does not short change herself with future relationships and situations, feeling she is not worthy. Something I wish I learned at her age! Good work addressing this, Mom!