how do i get emotionally close to a girl?

there's a cute girl who i really love and i've gotten pretty far with her; hanging out once a week, talking often, she said she feels like we understand each other.

but i feel like there's emotional distance between us. no matter how hard i try, i've never been able to become close to anyone in my life, not even my family or the girls i've previously dated. she's more jaded, so i doubt i can convince her to date me if i don't try to bridge that distance between us. i don't want to creep her out though. what do i do?