Unfortunately, once a material has been bleached, that color is gone forever. You can't wash out the stain. Your only option would be to try to dye the carpet back to its original color, which would be very difficult.
No a bleach stain cannot be fixed. It is a color remover. There is nothing you can do aside from getting new carpet. Bleach is permanent and nothing you can do will fix it. You might as well start looking at new carpet samples to replace your current carpet in your home.