I want to tell my gf to not leave the house without a bra
Why do you want to tell your girlfriend that?
I feel like since she belongs to me so she should do what makes me happy.
Your partner doesn't belong to you. You can't tell her what she can and can't do or dress.
She is my slave and I'm going to treat her as such.
Your partner is not your slave, they are your equal. You will both be much happier when you understand that.