I'm so sick of my annoying flatmate that I've started bullying her
What are you doing to your flatmate to bully her?
I secretly put her papers in the bin when she's not around
It's very rude to cause needless harm to another person, and you could really harm her if she loses important papers.  If she panics, then this will just end up being more annoying to you, so you shouldn't be taunting her like this.
Maybe I won't feel annoyed if she keeps quiet.
It's wrong to be rude to another person. She shouldn't keep quiet about what you did to her. She has every right to be upset with you for what you have been doing.