I need help with a girl

I moved to another city to start university last year, it was about a two hour drive from my hometown but it just so happened that a guy who lived there was moving into the flat next door, we pretty much instantly became best friends, he is a pretty good downhill rider and I have been riding bmx and mountain bikes for as long as I remember so we just hit it off.

Anyway a few months later, his sister who's his twin ended up in a psychiatric hospital as she was dealing with anorexia, and this kinda hit me hard because I spent my childhood in and out of these places before my father killed himself so I messaged her asking how she was to give her some support.

and have been occasionally popping up ever since and hanging out with her and her brother while I'm at home as she is recovering and rides bikes too, she's also a sketch artist too which is a plus. We seem to have a lot in common, not just hobbies, but traits like shyness and awkwardness, I've just become more and more crazy about her.

I've told her brother how I feel and he's okay with it, I've been hanging back to give her time to get better.

Im 21 years old and have never had a girlfriend, I think it's probably due to my shyness and anxiety (even though that's the quality I find most charming about her) and don't get me wrong I'm not too much of a looker.

I just want to know how I should go about getting to know her better and how I should persue eventually asking her out?

I don't want to miss a chance with her or scare her off

Right now she may just see you as her brother's friend, but asking her on a date is the moment of truth for you. Let your intuition be your guide about when the best time to do that might be. The eating disorder definitely adds another dimension to the usual "boy meets girl" equation. I'd steer clear of any dates involving meals until you know her triggers.

Ok, I think it's fine to hang out, but take it slow because of her situation. Don't come on strong or heavy. Make sure a crush doesn't get you ahead of yourself. Take this step by step and reflect each step of the way if she's even ready for dating.

popping up ever since and hanging out with her and her brother while I'm at home as she is recovering and rides bikes too, she's also a sketch artist too which is a plus. We seem to have a lot in common, not just hobbies, but traits like shyness and awkwardness, I've just become more and more crazy about her.