I can hear her farts every day
Are you going to help her with her farting problem?
I am going to shame her into stopping.
I understand that you are upset about her farting, however trying to embarrass her for something that everyone does naturally is not right.  Try to talk to her about what is happening and see if there is a way to fix the problem.
I'm not doing anything wrong here...
I'm afraid that you are doing something wrong if you try to publicly shame this person.  She might have a medical issue that causes excessive gas, and however much it upsets you, it is surely much worse for her.  See if you can help her get treatment, but if you can't, accept that the problem can't be solved.