It appears that you handled it correctly when she first disappeared, so well done! One of the hardest things in the world to do is to fight that annoying instinct to chase, but the correct response is indeed to not chase, let them go etc.
When a girl disappears like that she's used to having guy's chase her, when you don't chase eventually she will realise that if she doesn't do something about it, she'll never hear from you again and if she's still interested above 50%, she'll reach out and contact you in the manner that you describe here.
You also did the right thing by asking her out when she got in contact with you, but as she declined the offer really the only thing you can do now is wait, during which time you should be attempting to replace her with someone better. If she contacts you again just tell her it's awesome to hear from her and when is she free to hang out, if she declines again just ditch it. Always be polite though.
It's amazing who comes back when you don't chase, just last year I was seeing a girl and things were going great, then out of the blue she attempted to friendzone me... I said no, I'm not interested in that and get in contact with me if you change your mind, then nothing, nothing at all, gone from her life forever. 3 months later guess who comes running back
but by that point I didn't really want her anymore anyway as I as into someone else but it just goes to show how not chasing and doing nothing really can have the desired result although it may take time.
Again, well done on not chasing her, she'll probably get in contact with you again, but it's probably worth replacing her anyway, there's a million awesome girls everywhere