Yes, money is an appropriate gift for a bat mitzvah, but unfortunately I can't give you a dollar amount to shoot for. It varies according to how close you are to the family, how long you've known them, and so forth. If you decide to give a money gift, it is common to give multiples of $18 (like $36, $54, etc.) because the number 18 represents "life" in Jewish tradition.
If you're uncomfortable giving money, jewelry is another common bat mitzvah gift. A classic silver bracelet or earrings makes a wonderful gift that can last a lifetime. In fact, I still have several pieces of jewelry that I received as bat mitzvah gifts 20+ years ago that I still wear on occasion, and plan to pass on to my daughter in a few years when it's her turn.
It used to be common to give savings bonds, but I think that with interest rates the way they are, that's not a popular option any longer.