Time dependent density functionals are formulated and implemented in numerical simulations of the equilibration dynamics of an excess electron in superfluid helium. Previously developed density functionals that incorporate nonlocal potential and kinetic correlations and reproduce the dispersion curve of liquid He-4, are used. The electron-helium interaction is treated using pseudopotentials, after testing their accuracy in reproducing the static properties of the solvated electron bubble through its known spectroscopy. The dynamics initiated by the sudden compression of the bubble is dissected, and the results are favorably compared to classical hydrodynamics. In the near-field, the fast motion corresponds to interfacial compressional waves, followed by the slow breathing of the cavity. The far-field motion consists of a shock wave, followed by radiating sound waves. The solitonic shock wave propagates at speeds as high as 580 m/s, determined by the amplitude of excitation. The energy carried by the shock front ensures that the subsequent bubble dynamics occurs in the linear response regime. Dissipation occurs through radiation of sound during the acceleration stages of the bubble, carried by driven phonons of lambda=ctau=300 Angstrom, where c=240 m/s is the speed of sound, and tau=130 ps is the breathing period of the bubble. The interfacial waves generate traveling excitations at k=2 Angstrom(-1), high on the positive roton branch. Excitations in the roton well are not observed. The time dependent spectroscopy of the trapped electron is shown to provide a sensitive probe of the evolving dynamics by tracking the damped oscillations of the bubble, which is damped in two periods. The results are consistent with the related time-resolved experiments on He-2(*) Rydberg electrons, and significantly different from prior estimates of the electron-bubble relaxation dynamics.