Re: how would you go about this?
The reason you can work up a conversation is because you place her up on a pedestal. When shes in front of you you're acting star struck so you don't know what to say. It doesn't help that shes a shy person either it makes it that much more difficult for you. You need to practice just talking to girls, having conversations about anything. How is she ever going to know you if you can simply talk to her.
So here's your challenge: (random girls, not ones you're already comfortable with/ the girl you're chasing)
Day 1 - Say hello to 5 girls
Day 2 - Pretend to not understand something and ask 3 girls for help in a class
Day 3 - ask 3 girls a question and develop it into at least a 2 minute conversation
Day 4 - flirt with 3 girls (only counts if you get them to laugh)
*Day 4 bonus* do this in front of the girl you're chasing
Day 5 - have a conversation with and flirt with the girl you're chasing.
If you do more that's all the better but don't try to much and discourage yourself. The key for you is to take it in step so you can talk to girls better. Here if you need anything else.
In life you get what you put into it.