If you have mutual friends or work together, have the same class, etc, then you don't IGNORE her.
You just treat her like a random dude. You might say "Hey what's up." but whatever charm, or attraction (aka attention) you were showing her before is now cut off.
You don't want it to be like, "You were mean to me, so I'm not talking to you." You just want to separate yourself from a useless woman, move forward with other aspects of your life, and leave the girl wondering if you have found better options. Girls love attention, so when you take it away from them, it's gonna sting a little bit. But the real purpose is to move forward, not to worry about if you're re-attracting the girl.
So what if she catches on? She's not your wife. And if she was so damn worried about having you around, she would have dated you/f**ked you/whatever your goal was.
The issue is, You wanted the girl and she wanted your attention, but she didnt want to date you. Therefor, you've removed your attention from her and dedicated it to another alternative. It's not about "What if she realizes why..." because who cares what she realizes? Who cares what she thinks? Her role in your world was to be your booty call or girlfriend (or whatever).... and she didn't fulfill that role, so you're firing her and looking for new prospects.