The electronic absorption spectrum of the aqueous electron in bulk water has been simulated using long-range-corrected time-dependent density functional theory as well as mixed quantum/classical molecular dynamics based on a one-electron model in which electron water polarization is treated self-consistently. Both methodologies suggest that the high-energy Lorentzian tail that is observed experimentally arises mostly from delocalized bound-state excitations of the electron rather than bound-to-continuum excitations, as is usually assumed. Excited states in the blue tail are bound only by polarization of the solvent electron density. These findings have potentially important ramifications for understanding electron localization in polar condensed media as well as biological radiation damage arising from dissociative electron attachment.