My daughter's first encounters with a bully...

Let me start out by saying that this incident has occurred twice since the school year has started and it was only a push but it made me infuriated...My daughter is a first grader and a really good kid. She comes home one day and tells me that this girl in her class pushed her on the playground. So I ask, what was the reason that she pushed you and her reply is that she said the girl said she didn't want to play and she didn't like her so she pushed her and walked away. My first reaction was (right or wrong) Why didn't you hit the little girl (thought in my head...little ass) back? And she said that you are not supposed to hit people and that she didn't want to be a mean. I explained to her that I didn't want her to feel bullied and this girl is not a friend if she treats you like this. I told her that the next time it happened I wanted her to either tell the teacher what was going on or (if a teacher wasn't readily available) I wanted her to stick up for herself (hit the little shit). She felt very uncomfortable with that and that made me worry...Should I tell my daughter or son for that matter to hit the bully back?? That is what I was taught when I started school. I know times have changed and violence isn't the answer (or is it?) but I can not stand the thought of someone making my child feel bad or hurting them? So I can't say that I gave her the best advice but I can tell you that when I grew up that approach worked for me and when show that person you aren't going to be pushed around for the most part they back off!! So how have you handled this issues with your little ones??