Here are two ideas, perhaps the first one could be so much better in Thinking Particles, but the idea is already clear with the Standard Particles. Perhaps a little bit messy (mesh-wise) but as a quick and easy set up, I liked to share it.
The two other files in the folder (…_01.c4d and …_11.c4d) are the same, except, that _01 contains only the core idea, and _11 a set up.
In short it takes the point Y values of the spline and mirrors the start and end to “Mix” the bounce (see HUD) into the resulting spline W+B
As this might sound all cryptic, more or less, here is a one minute clip, showcasing the main parameters:
I hope that works for your project, at least as a starting point.
All the best
P.S.: It is doable to have the Bounce wave set up in a second Spline/Effector set up, (sync the speed via XPresso)
The scene file below is much simpler in the set up. I have two combinations for the wave and for the bounce (<——and——>)
Or more wave-like:
More clear, but perhaps to sharp:
A pure Shader animation: