Just ask her; simple as that. If she's single, she'll take it as a possible sign that your interested. If she's not single... then at least you know she's not single.
You don't have to literally go up to her and say "do you have a boyfriend?" Just when you're talking to her casually throw the question in, "so, do you have a boyfriend"? If she says no then she's all yours.
I don't know, it still feels too blunt, and I don't know if I have the courage to just ask a question like that
Oh, what are you whinging about?

Some of us have
never gotten even close to having a relationship. Just ask her if she has a boyfriend, maybe ask her out. Make it clear you're interested in a relationship. If she agrees, great! If she doesn't, then accept it and move on. It usually takes a few months, but you'll get over it eventually. Consider yourself lucky to have this opportunity and take it.
I know I know, before I met her I would have said the same thing if people were whinging about a relationship in this thread. Its just, gah, I don't know, its very confusing and hard to read, and I'm back at the point where I'm questioning if I'm just imaging things or if there's something there. I just think its too early in the (possible) relationship to ask questions like what Owen said, so Imma move down there now.
Also, once you find yourself where I am, simply shrugging your shoulders and moving on isn't easy, especially since I was were you are now before this all happened. This is like my only shot in 18 years of anything with the opposite sex, I don't want to just shrug it off like nothing.
Consider that me quoting all of the rants.
Most important ask her if she has a boyfriend. Do like salty said, make it casual. Girls like it when you're direct about things like that
Ugh, maybe I have to do this. I don't know, it just feels so direct and blunt, and at this stage of this (possible) relationship, I don't want one comment to make it go awry. I guess I have the next couple days + the weekend to build up the courage.
Though I think I should be building up the courage for contact information before the boyfriend thing, I don't know.
Second most important thing. When you went on your date, did you formally ask her on a date, and did
you describe it as a date? It is my experience that girls do not generally realize these sorts of games guys like to play. Guys tend to like to take a lot of liberties with what things are. To a guy the two of you going to dinner alone is a date. To a girl, unless you explicitly say it is a date, it could be any manner of things from potential hookup to just having dinner with one of your good friends.
(Trust me on this, I've gotten into a fair few arguments/forceful conversations with my girlfriend about how guys work).
This is one of the reasons why I asked if you guys planned the next date during the first one. For one thing it is always a fantastic indicator of how the girl thought the date went. If she's eager to plan the next one then you're a definite keeper in her book. Plus then you've got her pegged down for at least one more date

. It's ok if it didn't happen, it certainly wasn't how my current relationship got started and we've been together for nearly a year and a half now.
It wasn't a formal thing like "you wanna go out", or "you wanna go on a date". Not at all. I think I mentioned before this was more or less evolving organically. Here's short-ish timeline of how things went down regarding the dinner:
Firstly, the week before Thanksgiving break, we both depart from class towards the same destination (thought taking different ways). About halfway there we both stop at the crosswalk, she notices me, comes over, and starts talking to me ("where you heading?" "do you live over here"? yadda yadda). I tell her I eat over at her dorm's cafeteria because I have a class a class soon and this is the closest place to eat. We walk together to the cafeteria, and as we get in line, she says she got a phone call from a friend, was going to talk to her for a bit, and would sit and eat with me if she found me. She doesn't find me and I eat alone.
Now, moving forward in time to this Monday. We walk together out of class and towards the cafeteria (I find out she has a class at the exact same time as me, so our eating schedules line up), and sit down and eat dinner together. Afterwards, we depart our ways to our separate classes. There wasn't any talk about eating together again or whatever, I assume because since we have the same class together and we know we'll see each other on Wednesday, and Monday again (when hopefully we can eat together and talk some more).
So I have no idea if it was a date, or if she considers it a date, or if the modifier date is even necessary for the advancement of this relationship. I've never been on a "date" before so I wouldn't know. Just the bluntness of asking someone out on a date doesn't seem to mesh with the way this is evolving, which is also why I'm being thrown to question the whole thing.
Third most important thing. And this is coming from definite personal experience. If and when things start getting serious (especially if you kiss, start holding hands, or in general start doing couply-ish things), make sure you have the talk. What do I mean by the talk. Sit down, talk to her about what's been going on between you two and what it means. Again, refer to above. Be specific, use the words boyfriend and girlfriend because a lot of times girls really don't understand where a guy is coming from. Even more important than that you and your ladyfriend need to talk about what the two of you expect out of the relationship. It doesn't have to be "OMG FUTURE WIFE" (certainly not), but it should be a general hashing out of the perameters of the relationship. Is it a purely physical dealie or something more romantic; are you in a committed, monogamous relationship or are you free to see other people. Also implicit in this, if you want her to be your girlfriend make sure you formally "ask her out". Having the talk does not constitute asking her out. Until you do that you are not a couple in the girl's mind usually speaking.
Great advice, but I think its too early for this type of stuff. And no, nothing physical has happened, and to be honest, I'm not really thinking in that mindset. I don't see her out of sexual desire but more out of love desire. Which is odd, or at least I'm surprising myself by thinking that way. I feel like sex or physical stuff will be just a formality in the relationship later on, as of right now, I just want to be with her.
If this goes anywhere though, I'll definitely have try and do this. Though once again the whole formal and directness of it kind of turn me off from it.
I say this because this was a snag I hit in the early stages of my current relationship. I was not specific and we were just kind of making out/snuggling/having sex a lot. The problem was that she was doing this with other guys before I came along and those were not relationships, so when we started getting intimate she assumed it was the same sort of thing. I assumed we were a couple. We had a talk, sort of, but neither of us was specific enough for it to mean anything. The result was that for the 4 weeks (another problem was this was right at the tail-end of the year) of the end of term we existed in a sort of limbo; I thought we were a couple but only until the year let up, and she essentially thought we were [copulation]-buddies, and had no intention of being in a committed relationship of any kind.. This led to a lot of stress in our early relationship as she appeared aloof and I assumed it to mean she was leading me on until she could quietly let the relationship lapse at the end of term; she didn't think anything was wrong. This limbo continued throughout summer (we texted continuously throughout summer, she visited for my birthday; I visited her later on), until finally it came up in conversation in August and she told me that she didn't consider us to have been dating that whole time. I finally formally asked her out in early August, nearly 6 months after I had considered the relationship to have begun.
Moral of the story folks, be direct; don't ever assume anything in a relationship.
Yeah, this is the reason for all these whinging posts. I'm just constantly doubting everything because the way it evolved is very organic and not direct, so its all fuzzy and confusing and I don't know. The organic approach is the most comfortable approach for me (and the way I always hope to get into a relationship), but its also the most grey and confusing. Ugh, I guess I brought this on myself more or less by not formalizing anything early on and just riding along every time she and I started to talk more and more.
Thanks for all the help guys, even though I didn't ask for it you provided. I have a couple days of (tough) not talking to her to try and build up courage for something. I think I'm going to aim for contact ability outside of class, that way I'm not restricted in the time I can talk to her, and I can set up possible future meetups (as well as keep in contact over winter break when she's in France). After that maybe I can bring up the boyfriend girlfriend thing if I have the chutzpah to do so, I'm not sure I do at this point though.
Your guys' experience might be the saving grace of this whole affair

I feel slightly better that I have some sort of gameplan now, though the tough part comes in the courage aspect and actually following through with it. I'm hoping her continued approaching of me isn't some sort of tease and that she's legitimately interested, if its the former then I'll be incredibly disappointing and hurt, even though it would be my fault for seeing things that weren't there.
Thanks again.