Next time you see her walking in the hall way, shoot the s**t with her a little bit. All you need is two minutes!! Then, tell her "you know what? you're kind of fun, give me your number (take your phone out and physically give it to her) and we'll grab a cup of coffee soon."
The first 2 minutes you have with any woman is what is going to carry you through to a date. Hopefully she liked what she saw initially!
If she rejects you, cross her off the list for good and don't think about her again. Next!!
Once you realize that it's the first 2 minutes of an interaction with a woman that is what's going to get you a date, you begin to massively devalue your interactions with women you approach with romantic intentions. Once this massive devaluation occurs, rejection carries MUCH less of a zing and almost becomes something funny. With my friends that *get it*, we sometimes brag about how bad our rejections are.