  We report magnetotransport properties of BaZnBi$_{2}$ single crystals.
Whereas electronic structure features Dirac states, such states are removed
from the Fermi level by spin-orbit coupling (SOC) and consequently electronic
transport is dominated by the small hole and electron pockets. Our results are
consistent with three dimensional (3D) but also with quasi two dimensional (2D)
portions of the Fermi surface. The spin-orbit coupling-induced gap in Dirac
states is much larger when compared to isostructural SrMnBi$_{2}$. This
suggests that not only long range magnetic order but also mass of the alkaline
earth atoms A in ABX$_{2}$ (A = alkaine earth, B = transition metal and
X=Bi/Sb) are important for the presence of low-energy states obeying the
relativistic Dirac equation at the Fermi surface
