Where to go from here?

The situation has slowly improved since my original posting here about 3 weeks ago. Me and her have since been talking in class a lot more consistently, even feeling comfortable enough to share food with me. Right now it's mostly about school and other small things of insignificance, but considering where I was its a huge improvement. Tim has also become relatively passive since he was reported. Although he still talks to her and such, it's no longer about me at all and I have started to believe that maybe she's growing sick of him. Tim did attempt to discomfort me with the issue one more time in the last class, saying he'd pay her to go on a date with me an get to join his project group on class. When I overheard him and he repeated it, I thought he sounded ridiculous so I just laughed him off. Everyone else involved either laughed or just awkwardly moved on. It makes me think that maybe Tim is growing weaker with her and more desperate. At the same time however I'm wary of simply assuming this and I remain suspicious of him. What I'm trying to figure out is how to get closer to her (I.e number or something like that) without really making the mistake of last time in overdoing it. I want to get to know her better and talk to her outside of class above all else. Any suggestions?

That's great! & ask her out on a date! Set up everything make sure you will be completely available on that day and ask her a week ahead of time. So no one can beat you to it. Go to the movies so its casual but pay her ticket so she knows its not a friend thing. But don't let her know you are paying her ticket. Make it an in the moment type of thing.