STOPPING BLACK DYE FROM BLEEDING!? NEED HELP ASAP!?

I have bright red hair and am considering dying a layer underneath my bangs black. Now, I have worked very, very hard to achieve this red color and it is basically my baby. I get lots of compliments and what not all the time from random strangers. I would be heart broken if anything were to happen to my red. About two years ago, I had black hair and added platinum blonde streaks to it. The black, even though it had been died several weeks before, still bled into the blonde and turned it purple/gray when washed. I don't want this to happen to my red, so is there any advice anyone could give me on how to properly wash this so the black doesn't affect my red.

Also, I just bleached my roots yesterday, so if that would affect the black, please let me know. The box says it colors even the lightest blonde. But I'm not certain.

My hair is not in the best condition as I've died it a lot in the past. So I don't want to F it up and have to fix it. My hair probably couldn't handle that.

If you could direct me to a website that has any information on anti-bleed or if you could give me any advice on your own, it would be very much appreciated.

Thanks!