Polarized transient hole-burning spectra of the hydrated electron are calculated via quantum nonadiabatic molecular dynamics simulation. The underlying isotropic and anisotropic solvent fluctuations are found to relax on different time scales, leading to polarized spectral holes which are significantly more persistent than unpolarized holes. This separation of time scales leads to a clear spectral signature: transient bleaching in one set of polarizations and transient absorption in the other. This prediction can be directly tested experimentally.