Since the first 'buyer' didn't follow up, even after you emailed her the number, with a followup email no less, then she loses out, she had her chance. First come first served in this case, wouldn't you say. You certainly aren't going to turn down a sure sale. Just be careful you don't have two listings running at the same time for only one item available.
Setting up a private auction may have been a better way to set this up, to avoid this problem. Can't advise on that really, since I have never done one. However, in this case, since your buyer appears to be a 'no-show', what you did may be for the best if it results in a sale.