Removing black hair dye is a tricky process, and if it's permanent the process gets trickier. The best way or method is to let nature of our body do it's work, what do you mean you say, let your natural black hair outgrow the black dyed hair. If you in a hurry or your annual dinner is just round the corner and your need a quick hair do, bleaching with chemicals is the only way to go. Bleaching is a straining process, not for you of course with you sitting on the salon reading magazines with air conditioning; but to your hair.
Bleaching makes your hair stretchy and thin, as bleaching bleaches away the black dye and the outer layer of your hair making it fragile. If it's done in a non-professional matter your hair may come loose on your comb, don't get frighten like you got cancer. The main caution when removing black hair dye is that so it is to be removed evenly. After the bleaching process a toner is recommended to be used as this would reduce the orangey tone of the hair. It also acts as a conditioner for the hair preventing further damage.
Other options are also available to be used for removing black hair dye, which is to use other colored dyes to remove it after some mild bleaching and shampooing. A mixture of powder bleach and shampoo/conditioner is used, whilst preparing the mixture with equal parts of water. A creamy consistency or mixture is to be obtained after a mild mixing of the ingredients is done.
The mixture after been applied evenly and quickly slows down the bleaching process that actually strains the hair. This process is to be done at salons with people who are professionals in such fields, but for people that are equip with enough knowledge and practice it can be done at home. The time frame which the mixture is left on the hair is also a vital factor, if a short duration is at hand it would make the process easier but the whole process would take a much longer period of time as several trips are needed to complete the whole circle of process.
Black hair dye has to be dealt with respect, as it is difficult to be removed from any surface including skin and fabric. Applying Vaseline along the hairline is a good idea for prevention. Several other ways of removing black hair dye like rubbing cigarette ash, dipping milk in cotton balls, using WD-40, nail polish and hair spray over the stained area can also be applied.