To "bad mouth" someone when is to say bad things about that person. Example: "You are one of my best friends. I would never bad mouth you."

You bad mouth a person when you talk about that person in a bad way. Example: "Has she been bad mouthing me again?"

To talk badly about some thing is to bad mouth it. Example: "I heard you have been bad mouthing me." Another example: "Don't bad mouth our school."