Red dye is notorious for fading fast, a friend of mine used to keep her hair bright red just by dyeing it every few weeks and using color masks/toning conditioners. I don't think there are any other options, red dye just tends to fade and needs to be freshened up constantly.
If you dye it brown first, the red wouldn't be bright on top of it, more of a purple/auburn color depending of the tones. And from experience I can say that bleached hair likes to fade quickly no matter the color that's put on top of it, but it's not impossible to keep it looking nice!
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