Ok, so a little back story. This semester is my first in college, and I had a really hard time making friends. I always sat alone in the cafeteria, and was always by myself. Anyways, one day I recognized a girl from the hall I live in the cafeteria, who was also sitting alone, so I asked to sit with her, and she said “no thanks.” It really hurt so I just sat by myself like I always did holding back the tears.
Anyways, flash forward to now, I have finally made some friends, but I don’t think she has. I’m still hurt that she said no to me asking to sit with her. But I always see her alone, and I feel bad for her that she doesn’t have friends, but at the same time, I feel like I shouldn’t since I tried to be friends. So, should I feel bad for her not having any friends?
Maybe she has some…maybe she doesn’t but doesn’t want any…maybe she’s lonely. None of these options really have anything to do with you. I’d just forget about her, never mind about feeling any one way or the other.
Maybe she’s an introvert. Maybe she just doesn’t like people. Maybe she likes to eat alone.
You tried reaching out. That’s all you can do. No, I wouldn’t feel bad.
When my daughter was in middle school, a kid she wasn’t friends with sat at the lunch table with her and her friends. These are really nice kids and they tried including him in their conversation until he testily said “I sat here because I didn’t want to talk to anyone!” It was actually kind of funny. My guess is he is somewhere on the spectrum and really did just want some peace and quiet during lunch.
Anyway, specific to your situation, I would say you could ask her sometime if she wants to sit with you and your friend. She may or may not but the truth is you only can control your own behaviors. Her reason for saying “no thanks” previously may not have been intended to slight you but something wholly to do with whatever her own circumstances are, you really can’t know. All you can know is that you may continue to feel badly for not inviting her now.
Feeling bad for someone who doesn’t have friends is normal and healthy. Feeling ambivalent because she rebuffed you before is also normal. The fact that she hasn’t taken up with another group in the dining hall since then should tell you that it wasn’t anything personal against you.
Ask again. It’s bugging you the way things are now. If she says no again, you move on.
tmcnulty, I think you can feel really good that you did something brave. You reached out, which is hard to do when you, yourself are lonely and probably wishing someone would ask you. You recovered from that and went on to find people who can appreciate your company, which is great! It’s because you are an empathetic person that you worry about her, or what you should do, but she has her own choices to make.
Maybe now she regrets not taking you up on the offer, or maybe, as others have said, she’s comfortably introverted. Maybe she’s very particular (or narrow) about who she interacts with (and that doesn’t mean anything about you or your attractiveness as a friend. ) Maybe she’s depressed or going through something that she wants to deal with alone. Either way, she’s got to navigate her own choices. If you feel like it, send a friendly look her way, so she knows the door is open, but you have no responsibility for her decisions and she may very well prefer to keep her distance. . Enjoy your new friends and the whole college experience 
You’re sweet to want to help but leave it alone. You tried.
You can’t save the world because part of the world doesn’t want saving.
You made an effort once. It is a nice thought but I’d leave it alone at this point.
You can ask if she wants to join you. The worst that happens is that she says no thanks again. Don’t take it personally if she does, though.
What has got you feeling unsettled is not knowing enough about her to understand why she rebuffed your first attempt. Perhaps she was terrified when you approached her initially, or having a really bad day for unknown reasons - perhaps bad news from home. Don’t take it personally. Don’t blame yourself - unless of course you hadn’t showered before your first attempt…
It is normal to wonder about things like this, especially since your heart was in the right place.
You might consider dropping off a handwritten note to her, explaining that you are not trying to pry into her situation, blah blah blah, but since you do have something in common - you often eat around the same time - you just wanted some additional company, to break the loneliness, etc. I’m not sure if I would get into how you felt hurt the first time you asked to join her, how you understand how hard it for some of us to meet new people, how you wrote about this experience online at CC, and had a creepy middle aged lady you have never met give you advice blah blah blah…
I hope this story ends one a positive note for all involved, and it turns out that this person is not a terrorist plotting horrible things…
Best wishes.
What a nice gesture. Does she seem sad or depressed? If so, it can’t hurt to ask again. I personally would, and if rebuffed again, would just let it go. You could always say " thought it would be nice to get to know you better becasue we live in the same hall." Perhaps ask when you see her in the dorms though. Maybe she felt conspicuous being approached in public and she had a knee jerk reaction.
That was a very nice thing you did. Some people just don’t want to be bothered when they eat; I’m one of them. In college, I always ate at odd hours so that I could avoid eating with people. I still do it now; the building across the street from my office has a cafeteria, but people from my office often eat there, so it’s out of the question for me.
You could try once more if you really want to, but then drop it. I would not recommend a note such as @3puppies suggests.
It was a nice thing to do, but the girl told you she wanted to be left alone, and at that point I would leave it at that. You have a kind heart and are concerned she doesn’t have friends (or so it looks), but asking again will likely only annoy her at someone ‘butting in’ and won’t solve anything. You did what you could, and at this point it is up to her. As others have written, it could be she likes being alone when she eats, maybe she has friends who don’t go to the school, or maybe her friends don’t eat at the same time she does, there could be a lot of reasons, and in the end you can’t change any of that:).
But she could have had one bad day (maybe her dog or grandparent was sick, or something else had her really bummed). Or it was an immediate reaction that she was sorry about afterwards. Or maybe not. But there is no harm in asking.
^This. I’d definately reach out again. With all the stories of freshmen feeling out of sorts and having no friends to sit with and engage with, how can it hurt? I’d want someone to re-approach my D if she were in those shoes. And thank you! We need more kind people like you. If she scorns you again, let it be but my bet is she’s going to take you up on your offer. Let us know?