Is it okay to test my co-worker's hygiene without their knowledge
Why would you want to test their hygiene?
She is a bitch and she stinks a lot
I don't think you should be this mean about your co-worker's hygiene. If she finds out you're testing her hygiene, she may find that a bit creepy.
I will stare at her and watch her to see how she reacts to my staring
Do you really want to make your work environment uncomfortable like that? Staring at her will only make her uncomfortable to be at work, and that could lead to a tense environment. I suggest that you just leave her be and focus on your work instead.