Take baby steps, use words from your own mouth, and assume that she has a say, in this, too.
It is a fact of life, that they can refuse the best people and accept the worst. Someone is making a choice. They are deciding whether to put up with you, no matter how clumsy you feel.
If she will not send clear signals, or not reciprocate, there are still plenty of fish in the ocean, as they say. What I am saying is she has to meet you halfway, or isn't worth it.
I would tell people keep it dignified. Remember not to give yourself a bad name. But, never worry about someone like that, if it comes down to it. She has to make just as much an effort as you.
Now, then, what is a polite way of complimenting the person, and what would you like to do about that.
The rest is a coin toss. The situation will speak for itself.
But, you have my congratulations for trying to initiate. Most people in my life have been cowards, so wouldn't even try to get that ball rolling. Good for you.
It is considered vulgar and rude, to keep score in a social relationship, as we are supposed to be altruistic and charitable. But, as a coping mechanism, I have found it valuable to see what kind of responses I get.
Remember --
You said A.
She did B.
It fits a logical pattern.