The trigonal compound EuMg2Bi2 has recently been discussed in terms of its topological band properties. These are intertwined with its magnetic properties. Here detailed studies of the magnetic, thermal, and electronic-transport properties of EuMg2Bi2 single crystals are presented. The Eu+2 spins 7/2 in EuMg2Bi2 exhibit an antiferromagnetic (AFM) transition at a temperature T-N = 6.7 K, as previously reported. By analyzing the anisotropic magnetic susceptibility chi data below T-N in terms of molecular-field theory (MFT), the AFM structure is inferred to be a c-axis helix, where the ordered moments in the hexagonal ab-plane layers are aligned ferromagnetically in the ab plane with a turn angle between the moments in adjacent moment planes along the c axis of approximate to 120 degrees. An alternate but less likely magnetic structure is a planar structure with nearest-neighbor Eu spins aligned at approximate to 120 degrees with respect to each other, where these ordered-moment layers are stacked along the c axis. The magnetic heat capacity exhibits a lambda anomaly at T-N with evidence of dynamic short-range magnetic fluctuations both above and below T-N. The high-T limit of the magnetic entropy is close to the theoretical value for spins 7/2. The in-plane electrical resistivity rho(T) data indicate metallic character with a mild and disorder-sensitive upturn below T-min = 23 K. An anomalous rapid drop in rho(T) on cooling below T-N as found in zero field is replaced by a two-step decrease in magnetic fields. The rho(T) measurements also reveal an additional transition below T-N in applied fields of unknown origin that is not observed in the other measurements and may be associated with an incommensurate to commensurate AFM transition. The dependence of T-N on the c-axis magnetic field H-perpendicular to was derived from the field-dependent chi(T),C rho(T), and rho (T) measurements. This T-N (H-perpendicular to) was found to be consistent with the prediction of MFT for a c-axis helix with S = 7/2 and was used to generate a phase diagram in the H-perpendicular to-T plane.