We report the electronic and magnetic properties of stoichiometric CeAuBi$_{2}$ single crystals. At ambient pressure, CeAuBi$_{2}$ orders antiferromagnetically below a Néel temperature ($T_{N}$) of 19 K. Neutron diffraction experiments revealed an antiferromagnetic propagation vector $\hatτ = [0, 0, 1/2]$, which doubles the paramagnetic unit cell along the $c$-axis. At low temperatures several metamagnetic transitions are induced by the application of fields parallel to the $c$-axis, suggesting that the magnetic structure of CeAuBi$_{2}$ changes as a function of field. At low temperatures, a linear positive magnetoresistance may indicate the presence of band crossings near the Fermi level. Finally, the application of external pressure favors the antiferromagnetic state, indicating that the 4$f$ electrons become more localized.