Single nanoparticles are shown to develop a localized acoustic resonance, the bouncing mode, when placed on a substrate. If both substrate and nanoparticle are noble metals, plasmonic coupling of the nanoparticle to its image charges in the film induces tight light confinement in the nanogap. This yields ultrastrong "acoustoplasmonic" coupling with a figure of merit 7 orders of magnitude higher than conventional acousto-optic modulators. The plasmons thus act as a local vibrational probe of the contact geometry. A simple analytical mechanical model is found to describe the bouncing mode in terms of the nanoscale structure, allowing transient pump-probe spectroscopy to directly measure the contact area for individual nanoparticles.