It sounds like she enjoys your company and that you two are close enough that she trusts you to care for her. I think your best bet would be to invite her out to do something, but don't necessarily call it a date. I'm a girl and I know that when some guys have asked me out, hearing the word "date" made me want to head for the hills. There's a lot of pressure when you're on a date, to be on top of your game and to be extra mindful and impressive, and I think focusing on the fact that it's a date can take away from the fun of just enjoying each others company and can add a level of stress.

Before you ask her out, figure out what she likes to do. If she's been talking about a movie series she likes and you know the new movie is in theaters, mention to her that you'd like to see it (if you do want to see it) and that it'd be cool to have some company. If there's a local event happening where you live, say that you were thinking about going but don't want to be weird by yourself and suggest that she come along and enjoy it with you. If things turn flirty while you're out, then that's great! But if they don't or if she turns you down, always remember to be respectful of her choice and to let her know that you'll still be her friend.

Good luck with it all, and give an update when you can!