Dyed hair black and now i need help..?

so i dyed my hair black about 3 months ago and now i want to dye my hair a reddish/burgundy tone. i bought L'oreal Feria haircolor (the power red, "blowout burgundy"). is it necessary to bleach my hair in order to get the best results? or it is fine if i just apply the dye over my black hair?