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It depends on a lot of factors, pH is a big one as mildly acidic water and soil destroys bone very quickly.
Water logged conditions are actually, generally, very good for preservation as there is reduced oxygen slowing or stopping a lot of microbial action. Additionally there is protection from the elements (wind and freeze thaw, sun bleaching etc) that quickly erodes even metals. How quickly things get covered is a major part of preservation.
So there is no hard and fast rule about how long skeletons can last, everything from hundreds of millions of years (where fossilisation gets involved) to bones being destroyed in a year or two. There is branch of archaeology devoted to this called taphonomy (the laws of burial).
Source – archaeologist who specializes in bones.