Low-energy electronic structures in MnBi (=alkaline earths) are investigated using a first-principles calculation and a tight binding method. An anisotropic Dirac dispersion is induced by the checkerboard arrangement of atoms above and below the Bi square net in MnBi. SrMnBi and CaMnBi have a different kind of Dirac dispersion due to the different stacking of nearby layers, where each Sr (Ca) of one side appears at the coincident (staggered) position of the same element at the other side. Using the tight binding analysis, we reveal the chirality of the anisotropic Dirac electrons as well as the sizable spin-orbit coupling effect in the Bi square net. We suggest that the Bi square net provides a platform for the interplay between anisotropic Dirac electrons and the neighboring environment such as magnetism and structural changes.