Rit Liquid Dye works real well on carpet.
I've done a whole room in my house with it! Rit is a permanent dye and It stayed and never faded.
And since I'm putting my MH up for sale I intend to dye all the carpet in the MH to give it a face lift! :C
And since your spot was bleached I'd take the color you decide on and put it on a white piece of cloth first and put it down on the spot to see if it matches your carpet before you apply it. So you can make adjusts in the color if needed. AND only apply it with a spray bottle.
Pick up one of those small plastic spray bottles. Put the dye in that. Make a templet using a pretty big size of cardboard so no overspray on your carpet make the opening the size of the spot you need to dye and spay the dye.
http://www.joann.com/rit-8-oz-liquid-dyes-1pk/prd11794.htmlGo to a local big box fabric store like Joann's etc, to buy it they have WAY more color selections then Walmart. Good luck I think you will be happy with results. :C