Help! (Girls Only Please)?

Alright so there is this girl in two of my classes that I like. She's in my math and social studies classes. I have talked to her a lot and I can say pretty confidently that we've become pretty good friends inside of school. This would be my first time asking her to do something out of school though. I want to inbox her on facebook asking her if she wants to go to the library and study together for our math final coming up since we have the next few days off from school. In this hopefully, we would go and stop to get lunch in between or go for a walk, etc. Is this a good idea to try and spark something without coming on too strongly? I also know that she is looking for a boyfriend because of her tumblr posts relating to the topic, one saying explicitly that she wants someone to ask her out. Its just that I'm not sure if shes all too interested in me although I'm pretty positive she liked me towards the beginning and middle of the school year, although at that point I still liked her bestfriend which pissed the crap out of me because I considered her off limits for the time being. Were both sophomores in highschool if it matters and were both generally nice people . Do you have any input? Is this a good way to try and start a relationship? Please share your opinions! Thanks in advance for all of your answers!