You did fine. You made the offer, then backed off. The thing you want to avoid is to come off pushy or that you NEED to hear what she has to say, i.e. you want to R talk.
I am also glad you didn't say "but honey, I AM your best friend" or something like that.
Last thing I wonder is if your sitch makes it awkward for you to give her a simple hug at a time like that without you OR her reading into it? If so, maybe you do that next time too. Sometimes that speaks volumes.
