Something that can be classified as "business casual" is generaly apropriate to a Jewish religious function.
Nothing provocative or controversial.
Hats (or scarves) on women in a Jewish setting signify marriage.
If you are not married and it is not too cold DON'T wear a hat.
If you are married - then please DO wear a hat (or scarf).
The official orthodox Jewish rule (followed also by many Conservative Jews) which defines apropriate modesty for women is that the clothing needs to cover the legs past the knees,
cover the arms down to the elbows,
cover the whole torso to the colarbones.
Something with straps which shows shoulders is NOT apropriate under this rule.
Jewish women who follow this rule always wear a blouse under a dress with straps.
HOWEVER
Many Bat Mizvas of people who are not particularly religious have a party component which has nothing to do with Jewish cultural concepts of celebration or modesty.
Best thing to do is to ask your friend who invited you.