Measurements of dielectron production in p + p and p + d collisions with beamkinetic energies from 1.04 to 4.88 GeV are presented. The differential cross section is presented as a function of invariant pair mass, transverse momentum, and rapidity. The shapes of the mass spectra and their evolution with beam energy provide information about the relative importance of the various dielectron production mechanisms in this energy regime. The p + d to p + p ratio of the dielectron yield is also presented as a function of invariant pair mass, transverse momentum, and rapidity. The shapes of the transverse momentum and rapidity spectra from the p + d and p + p systems are found to be similar to one another for each of the beam energies studied. The beam energy dependence of the integrated cross sections is also presented.