<human>: Summarize the given text in a few sentences.

I started seeing this girl about a month ago. We've had a lot of fun, and it's stayed quite innocent so far, but she's awfully flirty (lots of touching, laughing at my dumb jokes, lots of talking about sex, etc), which makes me think she's interest in more than just friendship. 

Additionally, we were chatting the other day and she mentioned some guy that was really into her, and how he "didn't just want to hook up," and how she isn't really looking for a relationship right now, which seems to suggest that she is looking for a FWB sort of situation. She then proceeds to continue her very touchy, flirty behavior towards me right after saying these things. 

I'm moving in a few months, and will be far too far away to continue any sort of relationship, nor do I really want anything too serious right now for myself. I'm considering asking her to hook up, but it's not really something I've done before and I'm not sure how to go about doing it. 

I enjoy hanging out with her; we've had a lot of fun in the past month or so. I'm trying to find a way to ask that won't be too... how do I say... off-putting. I'd like us to remain friends, but fooling around would be a lot of fun. 

Does anyone have suggestions on good ways to go about this? I'm not sure if it'd be better to ask in person, over the phone, text or FB message, etc. 

I've been leaning toward a FB message, since I can sufficiently explain my idea but with minimal investment from either of us. It'd be easier for her to just ignore it, too, rather than bringing it up in a face-to-face conversation, in case that's not what she's really into. What are your thoughts?
<bot>: girl is flirty, neither of us want a relationship, how do I ask her to hook up in a way that maximizes my chances of maintaining our friendship and hooking up?