You would have to first lighten your hair first before you can add in the red to your hair. That means that you do need to use some kind of bleach. Just putting a straight up color on black hair won't do anything. Black hair is just too dark to have any other lighter color show thro.
However, these days many haircolor brands have now made products that can both lighten your hair and deposit the color all in one step. These products contain both the bleach and the color all mixed into one. I would definitely go to a professional salon to get it done, because they will use better quality products.