How do i come about talking to a girl i have cles with?

theres this girl i kinda like and i have british liturature and chemistry with her.... im usually not shy about talking to girls but i just dont find it in me to talk to her for a long period of time.... im mean ive said hi or talk to her for a bit but thats it.... shes also shy but i think she could like me cuz i always catch her eyeing me... but right now i just want to tak to her more and befriend her cuz around april im having a military ball in my school and would like to take her.... so what kind of coversations can i come up with to talk to her more?....