I don't want to meet my father's new gilfriend
What about your father's new girlfriend makes you want to not meet her?
I just think it's bad for me to meet her.
It's okay not to want to meet a stranger who you've never known. She is replacing your mother so it's normal to be conflicted about meeting this person.
I don't care about this new bitch. I should have a right to see my father and my right is more important than hers.
You don't have to see her, but it is important that you allow your father to have love if he wants it. How would you like it if your father said he didn't want you seeing some guy that you really like and care about?