Black duck, if you think she likes things casual then you should do it that way, but you can find out more about that by changing the topics to relationships. One thing I'm working on is asking "Are you a relationship type person?" and seeing how that convo goes. Any conversation that gets her to talk about her exs is good, like how they were too clingy, or how lovely it was in a steady relationship. That way she'll communicate what she wants. Still you have to stand out from the crowd in either case though.
Though GirlfriendOfAPUA is right - what you described sounds more like she's actually into you. So I'd say get some conversations going. Try to word them in a way that would keep your position neutral (don't make it sound like you're asking for a relationship, or a FB, see if you can keep it neutral) By the kinds of things she says in her response, she will let you know how she feels at that time. I say "at tha ttime' because, just like GFOAPUA said, feelings end up changing over time in casual relationships - I think most relationships should start of casual anyway, and then get serious. So be ready for this, and start particular conversations when you are unsure how she feels about it, to find out.
Do not say "We should hang out sometime." that's my advice - you could onlyi get away with that in real life, if you conveyed a lot of awesomeness thorugh your body language and tone of voice when you said it. Txt and chat is pretty bad IMO, avoid it when you can. Escalating a proposition to a phone call makes it a million times more possible she will say yes, when you opening with a frendly "how you doin" and get her smiling and talking before you even ask anything. Text loses all that, and also you are just saying "hang out" which is an IOI but not much incentative behind it.
Call her first, try your best to find an excuse to do something together based on what you both talked about - BUT, if the sexual tension is there, and very strong, and still no excuse to hang out is obvious... then you can just say "Hmm we should hang out sometime" with a huge smile in your voice - basically the frame of mind is that - This girl excites you, but there's no excuse yet, so you're just saying it, instead of finding an excuse.
If she really likes you (which she obviously does) she will say "Oh... what did you have in mind?" and that's when you pull out some fun activity you thought of earlier - and make it sound like you just thought of it then.
If she really likes you she will do pretty much anything with you. Eg. mini-golf "ah my friend told me about this silly mini-golf place they had fun at, I'm looking for someone to go with - we should check it out"