What does it mean for bones to be bleaching?

"Bleaching"—or more accurately, "whitening"—is a natural process that exposed bones and other materials undergo in certain climates. Here is a brief description of how this works, from "What Is Whitening and Why Do It?" posted on the bonedork site on tumblr:

The natural whitening process [of bones] is a collaboration between time and the elements. Ultraviolet (UV) radiation, which comes from sunlight, is a big player in this process.

The energy in UV radiation causes the degradation and eventual breakdown of many of the organic compounds that will stain bone tissue. As the molecules in the stains absorb solar energy, their electrons become excited and the bonds between atoms are more likely to break. Naturally, this means that in places where the sunlight is more intense, such as deserts, there will be more UV energy to break the bonds in the staining molecules and the bones will whiten much faster. It is possible to find perfectly, naturally bleached bones in less extreme climates, but, just as with degreasing, the bones are likely to be destroyed before the process completes.

The choice of the word "bleaching" for this process undoubtedly owes a great deal to an imperfect analogy to clothes bleaching (which typically involves the use of a hydrogen chloride solution). Indeed, the term "sun bleaching" is widely used to describe the effect of sun exposure in lightening everything from human hair to clothing.

The bonedork site points out, however, that attempting to artificially replicate natural bone bleaching by soaking bones in chlorine bleach will not work:

IMPORTANT!!! While whitening is often referred to as “bleaching”, please bear in mind that the only safe thing to whiten bones with is hydrogen peroxide. Chlorine bleach is damaging to all body tissues, including bone! Bone tissue is also extremely porous, and bleach will seep into it like water into a sponge. It will break down the molecules of the bone tissue itself, resulting in fragile, crumbling bones that will eventually turn to dust.

In the deserts of Arizona and Utah, I have seen bones and, somewhat relatedly, deer antlers (which are composed of fused hair, not bone) that have been sun-bleached to a ghostly white. It's easy to see why the term "bleaching" caught on to describe the whitening that such relics have undergone.