I've attended only one bat mitzvah, that of a friend of my daughter, and I think they vary according to the type of congregation (Reform, etc.). However, that girl's parents gave instructions about dress because she invited such a cross-cultural group. Basically, modest dress: no shorts, no very short skirts, no sleeveless, no bare midriff, and so on. I think if one would wear it to a wedding in a church, one can wear it to a bat mitzvah in a synagogue.

My understanding--and my experience at the one I went to--is that money is always an acceptable gift. I think that a gift card to a bookstore would be fine, or a meaningful book if one knows the girl well enough to know what that might be. Other gifts I saw were things like purses and scarves and such.