A common thing to write on a Bat Mitzvah card is a note of congratulations. The phrase, "Mazel Tov!" can also be used, which is the Yiddish term for, "Congratulations." If the person knows the girl well, she should write something personal in addition to a short congratulatory phrase.
A Bat Mitzvah is for a young girl and is the equivalent of a boy's Bar Mitzvah. As with the Bar Mitzvah, it is a religious accomplishment that is considered very important in the Jewish religion. The young girl has worked very hard for this accomplishment leading up to the ceremony. The term Bar or Bat Mitzvah literally means "son or daughter of the commandment."
When writing a card for this occasion, it can be a brief or long message of congratulations, depending on how close the card giver is to the girl and her family. Gifts may also be given along with the card. A gift card or check is reasonable for a teenager. Gifts need not be religious in nature. A person who is not Jewish is still welcome at the Bat Mitzvah, and a gift and card are gladly appreciated. There are no special customs or phrases that one needs to learn to give a gift or card for this occasion or to attend the ceremony.