Here's a big difference between nature and a natural history museum: In the wild, when you find a skeleton of anything, it's seldom arranged in a neat, orderly, anatomically correct manner. Even if an animal dies in captivity, nature won't just conveniently produce a skeleton suitable for mounting.
So how do museums get the perfect skeletal specimens that you see behind glass?
The answer: Lots and lots and lots of tedious work. Plus the assistance of a few thousand flesh-eating bugs.
This video from the University of Michigan traces the creation of a bat skeleton, from a fleshy dead bat in a jar, to a neat, little set of bones in a display case. It's painstaking (and moderately disgusting) work. Sort of like building model cars, if the Ford Mustang had realistic organ tissue.
Thanks to Neil Shurley!