I've had two random encounters that were similar to that, but both were actually at the girl's directions not mine.
First time was in college and I hooked up with a very cute Asian chick at a party. She ended up coming back to my place and things were progressing nicely, but when I went to start fingering her pussy she stopped me and said she really wanted to but was on her period. I tried to convince her that we should fuck anyway, because you know, you can swim in the red river but just don't drink the water. But she wouldn't go there, but she said, very matter of fact, if you have some lube around you can fuck me in the ass if you want. Of course I jumped at that chance and fucked her perfect little Asian puckerhole raw in several different positions. She seemed to really dig me, but I don't know if she was embarrassed about it after or what, but she left the next day she never returned my texts. Oh well, too bad because she was really cute with an incredible body and obviously a fun fuck.
Second was a girl who was friends with my buddy's wife. They live a few hours away from me and I went down to visit right after a longterm ex and I broke up. We went out to a bar and her friend met up with us. We hit it off and started hooking up and next thing I know I am back at her place. We start messing around and when we were working up to fucking, she stops me and says she doesn't let just any guy fuck her in the pussy. Instant boner kill as I went from thinking I was getting laid to blue balls. But she proceeded to say she just doesn't ever want to risk getting pregnant even with condoms, but she still likes to fuck. I just stared at her totally confused and she said, well, we can fuck in the ass. No complaints from me. I railed her ass that night and again the next morning and the following night too.