Going dark without getting green

I am wanting to color my hair a soft black, but I am worried about getting a green tone with the current color. I bleached my hair back in March. I have since been coloring over that with an auburn brown, lots of red tones. The problem is that it fades out fairly quickly. My hair is currently a dark blonde/light brown. It has more of a golden tone to it now. I am wondering if I should do a reddish color first, and go over that with the soft black? Or do I not have to worry about a green tone at all and just do the black by itself? Thanks!