Joe, if I can offer any advice, on top of the many good points already made.
I've always tried to view a dating situation from a woman's viewpoint. [emphasis added]
Personally, I would make the first meeting over a cup of coffee. Maybe a Starbucks.
A short, open ended meeting, works well to test the waters.
Dinner is too much, too soon, for someone you've met briefly.
IMO, the fact that she didn't exchange email addresses,(she has yours only) or cell numbers, speaks volumes.
Previous advice has been good; though, Greg Gable has hit the nail!
Good Luck, in the future!
In my opinion, the highlighted sentence is the best thing said so far in this thread (and I do
NOT mean that everything else is bad). Think about how a woman is often hit on by guys who don't mean to do her any good, and think about how she cannot know whether you are a decent guy or not until she gets to know you. Take things slow, and, of course, never be pushy and be ready to move on if she isn't interested. There may be a good reason for her to reject you (e.g., already has a boyfriend, is a lesbian, has heard stories about you from your ex [either true or false stories], etc.).
And it is premature to say she has rejected you. Who hasn't ever lost a slip of paper, or been too busy with something to respond right away?
My advice is to make friends with women first, and then see if there is a mutual romantic interest later. This means that you treat them almost the same as men you meet (keeping in mind what is said above, as a woman isn't generally going to know what sort of intentions you have unless and until she gets to know you). That is what I did with my wife, and we have been very happy together for a long time. We are best friends, as well as being husband and wife. I don't have the problems so many married men complain about with their wives, and, frankly, I have little sympathy for most men who do, as in most cases, no one put a gun to their head to make them marry the woman they chose. They should have put some serious thought into the matter first. But I am getting ahead of your particular issue.
My advice is predicated on the idea that you are looking for a long term relationship, and if you are not, you will probably not like what I have to say.
From rereading your opening post, Joe Schmoe, I see that this all was just last Saturday. It is too early to determine if she will or will not send you an email. Wait at least a week, and make sure you are not using anti-spam software that will prevent you from getting her message. Given how unreliable email is, it is entirely possible that she has sent you an email, and you have not received it. Probably, that is not the case, but it is common enough of a problem that you should not rule it out as a possibility. Anyway, give it at least a week before you start to concern yourself about this.