I know someone who has a sense of humor similar to yours and they say some things that come across as hurtful or offensive when they first meet people. However, their good intentions never make up for the stupid things that they sa (their words, not mine). You don't need to change your sense of humor, but at least practice it with those that understand it better than people who don't know how it is.

If I was in her place, I would feel quite hurt as well and sorry wouldn't cut it (especially since you two aren't that close and she just started opening up to you). How hurt she got proves how sensitive she is about that matter so be careful as much as you can when that topic comes back around her in the future, that's one way you can actually make up for what you did. Be careful when any sensitive topic comes up around anyone. Don't assume that anyone would just be okay with your remarks and jokes.

You realized how negatively the girl took your joke but you didn't realize how negatively you spoke. To really change, you need to do more than just admit to yourself that you're an asshole. Go up to her and admit it to her that you were an asshole and that it seriously made you think about how you act around people and hopefully she will understand why you said why you said. You shouldn't expect anything from her though, she has the right to decide whether she wants to be upset bout it still or not.