Many people make fun of themselves as a way to cope with insecurities - it doesn't mean they will appreciate someone else joining in!

Of course you didn't mean to hurt her - but that's rather irrelevant. Someone likely doesn't mean to rear end another persons vehicle - but that doesn't mean they can go "oops my bad!" And not have to deal with insurance or anything. It was done. Harm was caused. The hurt party has every right to be upset. The offending party does not have the right to be upset with the person they hurt.

She sounds like a good person for still wanting to be friends - she's just keeping some distance. I'd probably be doing the same in her situation as my trust and comfort with the other person would be really shaken.