The bulb looks fine. I don't see any rotting, and there is no need for bleach. I would just replant. The lilies will continue to wither above ground, but you will have healthy bulbs for next year. Now you can keep the non-growing bulbs in a cool place outside, regardless of how much light it receives. If you can dig the pot into the soil to taker advantage of the cooler soil temperature, that would be great. Dug into the soil is a good place to stay all winter, too, but when it starts its spring growth you will need to make sure it gets the light it needs.
Remember, when there are no leaves to support, the bulb won't use much water.