It is best to let this girl go.
Though her behavior may seem confusing in that she replies to your messages but never initiates and sometimes looks at you when you aren’t looking, she has made it clear that she isn’t interested in dating you.
You have asked her out two to three times and she has turned you down.
It doesn’t matter if she was genuinely busy the first few times that you asked her out, she still turned you down without giving you an alternative date as to when she would be available.
When a girl turns down a date without providing an alternative date in which she will be available, it is often a very strong signal of disinterest.
Even though she seemingly gave you all the signs of interest when you first met her, she may have simply been looking for attention or validation.
She has had more than enough time to go out with you in the last two months since she broke up with her ex and hasn’t taken advantage of that.
She is just not interested in you.
It is best to let her go and move on.