We generate spin-polarized electrons in bulk GaAs using circularly polarized two-photon pumping with excess photon energy (Delta E) and detect them by probing the spin-dependent transmission of the sample. The spin polarization of conduction band electrons is measured and is found to be strongly dependent on Delta E. The initial polarization, pumped with Delta E = 100 meV, at liquid helium temperature is estimated to be similar to 49.5%, which is very close to the theoretical value (50%) permitted by the optical selection rules governing transitions from heavy-hole and light-hole states to conduction band states in a bulk sample. However, the polarization pumped with larger Delta E decreases rapidly because of the exciting carriers from the split-off band.