So I've been dating this girl for 3 months now. Why hasn't she asked me to meet her parents?

maybe she's not ready or is worried about what her parents will say

I'm like that and truth be told, it's an embarrassment issue. I love my parents, but they would embarrass the crap out of me bringing up stories from when I was little or even worse, talk about ex boyfriends. And my father especially would be friendly, but also judgmental. They just want what's best for me and with that brings a certain amount of protectiveness. I would just talk to your girlfriend and find out what the issue is. Maybe you can reassure her and ease some of her worries.

She's just not ready. Some people just need a little more time when it comes to meeting there parents. She doesn't feel that serious yet or maybe she's not getting along with her parents right now. Ask her.

Read my answer here to get further insight on your question

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Keep in mind that some people are ashamed or distrustful of their families.

I'm with Wally. Just ask to meet them. If she says no she'll probably give you the reason too. It's win/win.

just ask her '' I'd like to meet your parents '' its easy and simple.

Yea, it's normal. They may think you won't like their parents.

They're just embarrassed by them or don't like something about them, and don't want you to see.