Bones have cells. They are called osteocytes.
But, bones contain much more than just cells.
Our muscles, skin etc contain just cells. So, when we die, the cells will die, and micro-organisms decompose our muscles and skin.
But, our bones conatin cells, calcium and a protein called collagen.
Collagen is a very strong protein. These collagen fibres and cells are dipped in calcium, which makes our bones.
So, when we die, our bones will not be decomposed easily. This is because, calcium is a mineral (metal) and micro-organisms cannot decompose them. The bone cells and protein are inside calcium too.
So, due to strength of calcium seen in bones, our bones can last long for millennia. That is why we find bones as fossils.