She's not any different, J. If you are going to mention it, mention it when you are ready to ask her out properly. You mentioned it and waited to set something firm for when she gets back, she's back now, so do it all the way!
Letting a woman know your availability is in no way showing desperation. Maybe saying "I've got every day free it's yours to choose" looks desperate. Giving an option of one or two days, most certainly does not. It shows interest in getting to meet her. Which a woman also wants, you know?
And your view point is "she should be lucky to be out with you"???? I don't even have words. You are not chatting because she is lucky to go out with you! You are chatting to get to know each other, set up a date and see if you both mutually feel like it is something you would like to further pursue. She doesn't even know you to know if she should feel "lucky to go out with you"
J- if you really want a quality woman, you are going to have to approach this differently. take or leave my advice. That's fine. But I can't help but cringe reading some of this and I can't imagine what kind of women this is attracting.