C.A.
Tell her she can do that in private and only do that in her room. This is an important time of self discovery and evidently she is finding pleasure there so it is important that she not be made to feel shameful. This is also an important time to teach her about privacy and her body. If you see her doing that then take her to her room and tell her when she is done she can come out. (smile when you take her as if it is a totally natural thing, you are just moving her location to do it) If you are in public, try to deflect her attention and softly tell her "wait until we get home and you can go to your room". yes she is old enough to understand what you tell her about this. If you are embarrassed, she will be embarrassed. In public just shrug it off, many parents have gone through this and don't make a big deal out of it and she should be fine, just be consistent about where it is okay. My daughter was a little older and she started calling her privates her "girlfriend". So when I would see her starting I would say in a whisper "we can't play with our girlfriend here, wait till you get to your room" That way no one will understand exactly what is happening unless you make a big deal out of it.
C.