An intense, short laser pulse incident on a transparent dielectric can excite electrons from the valence to the conduction band. As these electrons undergo scattering, both from phonons and ions, they emit bremsstrahlung. Here we present a theory of bremsstrahlung emission appropriate for the interaction of laser pulses with dielectrics. Simulations of the interaction, incorporating this theory, illustrate characteristics of the radiation (power, energy, and spectra) for arbitrary ratios of electron collision frequency to radiation frequency. The conversion efficiency of laser pulse energy into bremsstrahlung depends strongly on both the intensity and duration of the pulse, saturating at values of about 10^{-5}. Depending on whether the intensity is above or below the damage threshold of the material, the emission can originate either from the surface or the bulk of the dielectric, respectively. The bremsstrahlung emission may provide a broadband light source for diagnostics.