The kinetics of electrons bound to shallow donor impurities in n-GaAs was investigated by saturation spectroscopy using the University of California at Santa Barbara free electron laser. The resonant photothermal conductivity from 1s–2p+ transitions was measured at intensities greatly exceeding previous studies. Saturation of bound-to-free photoionization transitions was measured from 0 to 4 Tesla. The 1s–2p+ resonant photoconductive signal shows a distinct intensity dependence caused by the competing bound-to-free transitions which saturate differently. Evaluation of the electron recombination kinetics allows us to calculate the transition time of electrons from the 2p+ level to the ground state, the recombination time of free electrons, and the thermal ionization probability of the 2p+ state.