Can you tell me how'd you handle it?

Almost 3 weeks since I’ve been debating whether to approach this girl, i see her almost everyday in the school library and im sure she’s more fantastic and beautiful on the inside than i’ll ever know. Im a junior she’s a senior about to graduate and i just moved to the school(2mnths ago). Im not sure if she wants me to approach her because i haven’t really got any signs but we made eye contact for a few seconds last thursday. I not afraid of talking to girls but I just feel like she’ll be leaving high school while at the same time i feel like im at a new school for a reason and i’ve got nothing to lose. would it be unrealistic to say that i’m not wasting time by approaching a girl im interested in and possibly hitting it off and continuing to build something meaningful? Or should i say * it because she’ll be graduating soon and what college girl would be interested in a senior in high school? i dont know???but i do know that i feel prompted to approach her and be the great guy i am?