Should I sit by this quiet girl's side in class?

I'm in college, and there is this girl in one of my classes that I have been interested in. She is very reserved and always sits by herself. When the class ends she always quickly leaves our room. This one time though, she waited a little longer and I went to talk to her, and she seemed friendly enough. She talked about her major, the teachers, etc. The next class, when she passed by me the way out, she just kept looking down and said nothing. Later that day, we randomly passed by each other again and she did the same thing, only this time I said hi out loud and she replied with a smile.

I was thinking about coming early the next day we have class together and ask to sit by her side, as she always seems to be in a hurry when she leaves. The only thing is, what if I'm bothering her? I mean, I only talked to her once, and for 5 minutes, but still she didn't even make spontaneous eye contact the next day we met. I fear that it would make her uncomfortable, which I obviously don't want lol. Should I take the risk?
Should I sit by this quiet girl's side in class?
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