Although the front spring has been suggested numerous times as the possible culprit for bouncing, I haven't seen the spring hangers (shackles) mentioned. If the bushings inside the bottom spring leaf eyes and the perches are worn - as they usually are from age and lack of lubrication - the shackles will be loose inside the bushings, allowing the front spring and axle to rock to and fro. This will cause changes to the caster of the front axle as the car moves forward. The rocking motion could manifest itself as a bounce as the spring rapidly moves back and forth. This may only kick in at the same speeds cited by the poster because the physical forces acting on the front spring and axle finally overcome static resistance offered by these parts. Any movement here will most certainly be felt in shaking, shimmying, wandering and probably bouncing.
Additionally, if the four nuts on the backside of the shackles are loose, this will also allow the front spring to rock, creating unwanted gyrations and effects upon the front alignment. Alternately, if the nuts are too tight from over-aggressive assembly, the spring will not be able to do its job, meaning to flex up and down in response to road conditions. You should be able to use a long pry bar between the top of the front axle and the shackles to see if the spring can move up and down. If the spring ends cannot be lifted using a pry bar, either the nuts are too tight or the shackles are frozen inside the spring leaf ends and the perches. Usually just one side has seized, which also causes the car to lean to one side or the other. By the way, if the ends of the springs are resting on top of the axle, the spring is fatigued or broken and cannot perform its function. Replace or repair the front spring to achieve the necessary gap between the top of the axle and the spring leaf ends.
When checking the shackles, also ensure that the four large nuts securing the front spring to the frame are tight and that there is no looseness between the spring U-hangers and the front crossmember. There were different styles and lengths of the U-hangers and thread lengths, depending upon year and number of spring leaves (heavy-duty versus standard number of leaves). If the wrong ones have been installed and the spring is loose inside the front crossmember, there will be movement that will translate into unwanted gyrations. Ensure that the correct U-hangers are in place and are tightly secured.
Marshall