BaSnO_{3}, a high mobility perovskite oxide, is an attractive material for oxide-based electronic devices. However, in addition to low-field mobility, high-field transport properties such as the saturation velocity of carriers play a major role in determining device performance. We report on the experimental measurement of electron saturation velocity in La-doped BaSnO_{3} thin films for a range of doping densities. Predicted saturation velocities based on a simple LO-phonon emission model using an effective LO phonon energy of 120 meV show good agreement with measurements of velocity saturation in La-doped BaSnO_{3} films.. Density-dependent saturation velocity in the range of 1.6x10^{7} cm/s reducing to 2x10^{6} cm/s is predicted for {delta}-doped BaSnO3 channels with carrier densities ranging from 10^{13} cm^{-2} to 2x10^{14} cm^{-2} respectively. These results are expected to aid the informed design of BaSnO3 as the active material for high-charge density electronic transistors.