The thermoelectric transport properties of CaMg2Bi2, EuMg2Bi2, and YbMg2Bi2 were characterized between 2 and 650K. As synthesized, the polycrystalline samples are found to have lower p-type carrier concentrations than single-crystalline samples of the same empirical formula. These low carrier concentration samples possess the highest mobilities yet reported for materials with the CaAl2Si2 structure type, with a mobility of ~740cm$^2$/V/s observed in EuMg2Bi2 at 50K. Despite decreases in the Seebeck coefficient (\alpha) and electrical resistivity (\rho) with increasing temperature, the power factor (\alpha^2/\rho) increases for all temperatures examined. This behavior suggests a strong asymmetry in the conduction of electrons and holes. The highest figure of merit (zT) is observed in YbMg2Bi2, with zT approaching 0.4 at 600K for two samples with carrier densities of approximately 2x10^{18}cm^{-3} and 8x10^{18}cm^{-3} at room temperature. Refinements of neutron powder diffraction data yield similar behavior for the structures of CaMg2Bi2 and YbMg2Bi2, with smooth lattice expansion and relative expansion in $c$ being ~35% larger than relative expansion in $a$ at 973K. First principles calculations reveal an increasing band gap as Bi is replaced by Sb then As, and subsequent Boltzmann transport calculations predict an increase in \alpha for a given $n$ associated with an increased effective mass as the gap opens. The magnitude and temperature dependence of \alpha suggests higher zT is likely to be achieved at larger carrier concentrations, roughly an order of magnitude higher than those in the current polycrystalline samples, which is also expected from the detailed calculations.