Tite Kubo, the creator of bleach, gave three reasons to calling it that.

One, as the soul reapers cleanse souls, it's like they are "bleaching" their souls. Like how bleaching in a clothes sense means to remove stains and blemishes, the shinigami remove sin and corruption from the souls.

Two, he wanted to name the anime black, but then decided it should be Bleach which suggests the color white, in that case would make one think about the color black.

Three, "Bleach" was the name of his favorite Nirvana album.