How do I talk to someone not in my friend group or any of my classes?

Ok, so I'm doing my A-Levels right now and there's this person I'm kind of crushing on (not a heavy crush or anything) I've said maybe 4 words to them. I really want to talk to them but I'm not in any of their classes so I can only see her at break and lunch and we seemingly have no mutual friends what so ever.
(me showing how we have no mutual friends)



Since her group is small and close then I feel it'd be really awkward for me to go in and talk to them as they seemingly know each other really well, she has no social media that I know of or that I use at least.
Even at break and lunch times it's hard to approach her if she's alone as she goes on her phone, she also seems to go to this club (idk what it is) so me stopping her would be annoying for her I assume. on top of all this she also seems to be shy, as am I, so this would maybe make her uncomfortable with me talking to her which I feel would make the convo awkward as neither of us would talk much.

Any tips are appreciated, and no I also don't see her after school, I take the bus and idk what she takes but I never see her after school so obviously she goes a completely different way to me.