The Juno spacecraft had previously observed intense high frequency wave emission, broadband electron and energetic proton energy distributions within magnetic flux tubes connected to Io, Europa, Ganymede, and their wakes. In this work, we report consistent enhancements in <46 keV energy proton fluxes during these satellite flux tube transit intervals. We find enhanced fluxes at discrete energies linearly separated in velocity for proton distributions within Io wake flux tubes, and both proton and electron distributions within Europa and Ganymede wake flux tubes. We propose these discrete enhancements to be a result of resonances between particles' bounce motion with standing Alfvén waves generated by the satellite‐magnetosphere interaction. We corroborate this hypothesis by comparing the bounce and field‐line resonance periods expected at the satellites' orbits. Hence, we find bounce‐resonant acceleration is a fundamental process that can accelerate particles in Jupiter's inner magnetosphere and other astrophysical plasmas. Plain Language Summary The passage of the Galilean moons‐ Io, Europa, Ganymede, and Callisto, perturbs the plasma flow in Jupiter's magnetosphere, creating waves that travel from the moon and reflect off Jupiter's ionosphere. These waves have been proposed to accelerate charged particles, and such accelerated particles had been observed by the Juno spacecraft during its passage through magnetic field lines connected to the satellite wakes. In this work, we find instances when this acceleration occurs selectively at specific energies that have constant separation in speed. We propose that this selective acceleration is due to resonance between particle bounce motion and the waves arising from the satellite wake perturbation. Bounce‐resonant acceleration is a promising fundamental process which can accelerate particles in Jupiter's inner magnetosphere and other plasma systems with similar geometries. Key Points Proton and electron flux enhancements in satellite and wake flux tubes often occur at discrete energies linearly separated in speed Broadband proton flux enhancements at <46 keV energies were also observed within satellite flux tube crossings Particles can be accelerated via resonance between bounce motion and standing Alfvén waves generated by moon‐magnetosphere interactions