Belittling and mocking them isn’t bullying them, it’s insulting them.
I get where you're coming from. The question is, do you want to help anti-vaxxers change, and stop being anti-vaxxers, or do you just want to feel superior to them?
If you want them to change, I really encourage you to think yourself about times in your own life where someone else successfully encouraged you to change their mind. Did they do so by mocking and belittling you, or did they do it with kindness and by helping you understand your mistakes in a way that didn't make you feel rejected?