How can I help my daughter overcome shyness?

My daughter is pre-school age. I go to parties with her where there are other kids, and she looks at the kids but she stands near me. Sometimes the kids come up to her and ask her to play, and she either huddles near my leg or wants me to go with her. I encourage her to go play with the kids, but she wants me to go, too.

At school, she’s fine because she knows all the kids. The teacher reports that she will watch the kids cautiously before jumping in to a group.

Just a side note, I’m not shy as far as meeting strangers (I do it for a living and have to ask them intimate questions, so no shyness there). In situations like in a store or where there’s a problem, I have no problem sticking up for myself. I’m not shy with small groups, but in large groups like parties where I don’t know anyone, I am shy. I will sit by myself before I go up to a strange group and introduce myself and “network.” Someone told me once it’s because at work I know what everyone’s roles are, whereas, in groups of strangers, I’m on shaky ground.

If she ends up like I am that’s fine. Everyone is different, and I understand that. However, for kids, especially when I see she wants to play with the kids, I would like her to not need to stand near me or have me accompany her.