Theres this girl i like but i dont know how to engage her in a conversation?

she goes to my school shes in the majority of all lmy cles. shes my age. shes beautiful. but im nervous to talk to her. im shy shes outgoing. she says hi to me a few times a week zand i enjoy talking to her because we have the coolest conversations but we have only talked about 3 or 4 times. i want to at least say hi and strike up a good conversation but im completely clueless on what to talk about. I dont want it to end up like every other conversation. I lack the courage to go up to her and do this. she means a lot to me because i dont have very much friends. i dont haver her phone number. what can i do? i want to show her im friendly. she already knows that but i want to make her feel special. I tink about this too much and i often make up an excuse of why i cant do it like im not looking my best