Should I even bother?

I have this problem where when I like a girl, I really can't stop thinking about her until I try to ask her out, and ultimately I get rejected. Until this rejection, I can't help but think about said girl.
Recently I have met a girl through an organization I joined in college, and I think I am starting to like her/ can't stop thinking about her. She is a junior and I am a freshmen. She is also the president of this organization. One thing I am afraid of, is if I ask her out and she rejects me, it will make this organization I go to very uncomfortable for a while, and it might even hinder me from moving up in the ranks.
However, my wanting to ask her out is based on mixed signals that I am getting from her (I cannot read girls for s***). Here are examples of why I think she might be into me:
A while ago, we went to a conference together through the organization. Near the end the conversation came up about housing for next year, and she said that we could room together in a gender exclusive housing option. This struck me odd because at that time I didn't know her too too well. I laughed out of nervousness, thinking it might be a joke. I still don't know if she was serious about it, and I am afraid to ask her.
Not too long ago either, I was supposed to meet her in the organization's office for a project we were supposed to try and do for the college. She moved the appointment to her dorm room because she had other work to do, and I went over there. She had another friend there as well. We all talked about the project, as well as me progressing through the organization. After, we all walked out onto the campus, headed in fairly the same direction. Her friend broke off and it was just the two of us. She then decides to share very personal information with me, things that she couldn't tell anyone else, and feeling like I should even the playing field, I shared some personal information with her. After that, she said that that is what we can do for each other, is be a person that we can share these things with. We eventually got on the topic of relationships, and she told me about one of hers, and I did the same. At this point she had to go to her class, but before she went, she asked me about a girl I hang around with, asking who she was to me. I told her the truth, saying that she wasn't my type, and that we were just friends. We said goodbye after I suggested we do this again.
The last part of this insecurity, is that a friend of mine said that she already likes someone (I don't know who).
With what has happened, I really can't tell if she would be interested in going out on a date with me, and I am too afraid of screwing up my progress in this organization, but most of all screwing up the friendship that we have entrusted with each other.
What should I do?