The Stepside box is the same up to '87 (with some varances), but the bumpers are only the same to '59. The '60-'66 bumpers, while a similar profile shape, are actually different and do not interchange. I have been told that the '58-'59 Fleetside bumpers are different from the Stepsides, being somewhat flatter in contour. I have never actually checked this myself, but have no reason to doubt it either.
If you're not concerned about using a factory bumper, and would be ok with a dealer installed type rear bumper, I would think that any up to '66 would fit alright with modifications to the brackets. The dealer style bumpers (Barden is a popular one) are relatively easy to find at the salvage yards, possibly moreso than a factory bumper.