Don't tell her radio silence or anything stupid like that... Just tell her your busy... It's not rude as it tell her why you're not responding... After that she will wonder if you are really busy or just blowing her off a little.... Don't be impolite to her but actively ignore her.... And once in while when she contacts you tell her the cool stuff you've been doing...

If she wants to break up, then she's manipulating you as a sort of "hold over" (some women do this for emotional reasons, sex, money etc.) don't give into her game... Show disinterests (don't fully ignore)....she won't respect you if go by her game...

My advice don't waste your time...

also with all the women out there consider if she's worth it