I have a black mazda 6 sw with curb side caused stratchs on the front black plastic bumper. I have the matching manufacturer touch up paint, but I wonder if there is another way to cover it up, like for example buffing, that would be more effective.

If the scratches are too deep, buffing won’t work.

What you can do is apply some touch up paint, leave it for a few days to cure and harden and then try buffing again.