Rare-earth free permanent magnet MnBi (NiAs-type crystal structure) displays strong uniaxial magnetic anisotropy above its ∼90 K spin reorientation transition (SRT). X-ray magnetic circular dichroism (XMCD) measurements at the Mn K and Bi L2,3 edges show induced magnetism in Bi, which is strongly coupled to the magnetism of Mn. Temperature- and pressure-dependent XMCD results reveal that hydrostatic pressure mimics the effect of temperature, driving a transition from uniaxial to in-plane anisotropy. The pressure and temperature transitions are shown to be connected to an anisotropic lattice contraction in NiAs-type structures. Temperature and pressure, hence, induce coupled structural and magnetic responses, highlighting the importance of both anisotropic lattice change and Mn-Bi hybridization in leading to the magnetic anisotropy change across the SRT. The dependence of magnetic anisotropy on the anisotropic lattice change is confirmed by density functional theory.