dpending on where the fracture is, it could maybe be fixed with some type of epoxy or glue. maybe try putting screws, in a unseen area if possible. if fracture i completely through try a decorative bolt in area, adding the same decor hardware on all four posts to match.
The most obvious option is to use wood glue. However, if the bed is not an important piece you might concider cutting down the bed post much like you would file down your nails if one of them broke. Once that done and they are all even again you can top with a new topper and have a new bed!
Depending on the severity of the break, ordinary wood glue may fix the problem. After applying the glue use clamps to keep pressure on it until the glue has cured. For larger breaks that are completely severed, you can drill holes in both ends and install dowel pins and glue.
A broken bed post can easily be fixed in some cases. Depending on where the fracture is you can restablize it so it will be sturdy again but if the fracture is in a critical spot or is a large fracture you may need to replace it.