Did you provide a specific day in order to go out or did you just say end of the week? How did you say you were busy? What did you say in regards to rearranging it? And by 'died a death' do you mean she didn't reply to you?

Suggestions/thoughts:

I never say hi first to girls on facebook unless Im talking to them for the first time. All other interactions made by us over facebook are started by her, period. I hate talking over IM to be honest so try and avoid it.

In future tell the girl you are busy 'this day' 'that day' 'this day' etc and leave a max of 2-3 days left where you are actually 'free'. Preferably in the evening.

I personally wouldn't have text her something as random as you did. It comes across as if your TRYING to create conversation rather than just letting it flow or it being spontanious, thats why I suggested texting something that would relate to her in particular as it adds a reason to why your texting her and not because you just want to 'create conversation'.