Okay, so I’m a second semester freshman at my college. Last semester I didn’t have a roommate due to her dropping out before the beginning of the semester or something. Anyway, this semester I was assigned a roommate. I was a bit nervous since I don’t have experience living with anyone other than my family. I thought I would just be polite and try to become friends or even just somewhat friendly with them since we’d be living together for 4 months. She moved in a day before me and when I returned to my dorm yesterday she barely talked to me at all. I thought that maybe she was just as nervous as I was so I tried to strike up some conversation and be nice. She seemed okay with it. I came back from my classes today and I guess she didn’t realize I was back because about 15 minutes into me being in my room I hear her talk trash about me on the phone with one of her friends. It was pretty muffled but I just heard her mention her roommate in an annoyed tone. I got really upset about it because I’ve been nice to her since I’ve met her. I’m a very tidy person so I don’t think she’s angry that I’m messy or something. I also keep to myself a lot and I even put headphones in when I’m playing a video game or watching something so I don’t disturb her. I really don’t know what I’ve done wrong. Can anyone give some advice on how to handle this? I don’t want to confront about something that may not be true and i don’t want to move rooms as we’ve only been rooming together for two days now.
Ask her to go to dinner with you and some of the other people on your floor. Baby steps.
If she is new to the school, she may be scared too. If she was switched over from another room, it may be because of conflicts with another roommate and mad she has to share a room. It will take some time to get to know you.
I should probably mention that she’s always on the phone with her friends on speaker or listening to music and I don’t want the bother her. It sort of makes me feel like she doesn’t want to have me try and talk to her and like I said I’m really withdrawn so I’m not that great at interacting with people. 
Your goal shouldn’t be for her to be your friend, but to peacefully co-exist.
Right now, I would pretend like you haven’t heard anything. When you go to dinner, ask if she wants to come along.
If you do a dorm activity, invite her. If you are going to a on campus event, ask her.
If she is on speaker, and it is bothersome, you could ask if she could take it off speaker. “Hey Julia…I am try to get through my Orgo homework…would you mind taking it off speaker?”
But do keep in mind your “so keep to myself a lot and I even put headphones in when I’m playing a video game or watching something so I don’t disturb her.” could be misinterpreted by her as trying to keep her out.
You could say “I am going to play some video games so I will put on the headphones so I don’t bother you. If you need anything just tap me on the shoulder.” Then you are showing her you are open to interaction with her.
Also, don’t assume she is trash talking you. You didn’t hear what she said.
Also food. If you have an opportunity to get a cookie or something, bring one back for her.
Ask her what classes she is in.
Seems as though your new roommate is trying to irritate you into moving out. Is that possible ?
Is she new to the school or maybe had a bad roommate experience first semester? I think sometimes people say ugly things when they are really scared themselves or nervous in a new environment. Like someone above said, take baby steps - ask her to go to the cafeteria with you or to dinner with a few other girls on your floor. Politely ask her to turn off the speaker if its bugging you or you are trying to study. Just give it a little while longer. You don’t have to be besties, but somewhere closer than co-existing would probably be nice. Hang in there!