I'm pretty sure that the Brad Pitt rule covers the "I've avoiding any relationship right now" excuse.
If she likes you, she will find time for you. If she doesn't like you, then she will use the excuse that she doesn't have time for any relationship.
You are in your 20's, act like it and just ask her out. Hell, for all you know, she is turning down the other guys in a vain hope that one day you will grab a pair and finally ask her out.
When I met my wife in 1997 we felt comfortable with each other because neither of us wanted a relationship. Now we have been married for over 13 years and we have 4 kids.
Males and females are naturally attracted to each other. When we say we don't want to be in a relationship at this time that usually comes with an unsaid caveat of unless the right person comes into my life.
Listen to what Shieldes says above.
The longer you wait the higher chance you have of being put in the friend zone.
Maybe she really is avoiding all relationships, no matter how tempting. It's possible, and maybe even a sensible choice on her part, if she has a lot to sort through in her own life. It may also be an excuse, or perhaps a bit of both.
Regardless, you will get nowhere by hanging around and mooning over her. If she's not into you, it won't help. If she's honestly avoiding a relationship for now, the guy she eventually decides to take a chance on won't be the one waiting patiently.
If you think she's a cool person and you just want to hang out some, that's fine, but don't harbor illusions that it will lead to anything more. And if you get over those illusions, you'll be able to talk to her, because you won't be worried about impressing her and will be able to converse naturally.
Shieldes is probably right that you should ask her out to be sure where you stand, just don't sit around and wait for her if she says no because she's "not ready for a relationship right now."
My wife was avoiding all relationships when we met. If you like her, go for it. Just be yourself and ask her to go places and do things with you.