Am I in the friendzone with this girl? Should I ask her out?

Casual day time meet-up, such as for a cup of coffee, or getting some lunch after a revision session i.e. something that would be perfectly normal to do with a friend. This will allow you to test the waters, see if you "click", and possibly set a precedent for a future meet-up if things go well.

Such a "date" has total deniability. If it doesn't work out, it wasn't even a date - just two friends having coffee; if it does work, then it was a first date.

See what I mean?

There's a girl in my drama society who I like a bit. I always found her attractive but we only really started talking properly a couple of weeks ago and that conversation really took off when I found out she was a massive Doctor Who fanatic, like me. We share pretty much the same level of knowledge, which is very high and we got on really well. At one point, she even said "it's nice to be able to talk to someone who knows about some of this stuff" or words to that effect, meaning specific details about the show that only true fans really know about. This was at a pre-drinks, but I had to leave early that night as I had an assessment the next morning. As I left, she said "you'll smash it!" and gave me a fist bump for goodbye. She was giving all the guys there fist bumps too. She would also say "hi" to me in passing before this and has since as well.

I just can't help but think that she doesn't see me in the way that I see her (a recurring situation for me). A girl I spoke to about it said that if she did see me in that way then she would have gotten up and hugged me goodbye when I was leaving, rather than fist bumping. That's fair enough considering she was fist bumping everyone else there as well, multiple times, although she only did that to me once as I was leaving and I've also thought about how the space was small and crowded too. I mean, I wouldn't have hugged her goodbye if I was in her situation for that reason, but that's just me.

She lives in the same court as me so I happened to bump into her on my way to drama society today and so we got talking about the play we're doing and then I mentioned a Doctor Who convention that I had been to at the weekend. The conversation went well but again I still can't help but think that deep down she only sees me as a friend. That's just a vibe I'm getting.

It's bad timing that this is happening now as we're coming to the end of the first academic year at uni, but because I do genuinely like her a bit, I have been debating with myself whether or not I should try to ask her out, or even just meet up, and see how that goes? It's practical meeting-wise considering she lives in the building right next to mine, but I just don't know whether I should or not. How would it look for her that I'm suddenly asking to meet up with her out of the blue? Suppose she says no and I still have to see her in drama society; wouldn't that be a bit awkward?

I just don't really know what to do or think right now and any advice would be greatly appreciated. Thanks!