Once a bird dies the dead bird should begin decomposing within one or two weeks.
But for the dead bird to fully decompose down to nothing but bones it can take the dead bird from 4 to 6 months to decompose fully to where nothing is left of the bird but bones.
If you find a dead bird it's best to use a shovel and pick it up and either throw the dead bird into the trash can or dig a small hole in your yard and bury the dead bird to prevent diseases from spreading from the dead bird.