Dirac semimetals of the form $A$Mn$X_2$ ($A=$ alkaline-earth or divalent rare earth; $X=$ Bi, Sb) host conducting square-net Dirac-electron layers of $X$ atoms interleaved with antiferromagnetic Mn$X$ layers. Hypervalent pnictogen square nets have long been predicted to host an electronically driven Peierls instability, whereas low-temperature anomalies in CaMnBi${}_2$ near $T^{*}\sim 50$~K have previously been discussed in terms of possible magnetic canting, TRS breaking, and a resulting Weyl-semimetal (WSM) state. Here we use polarized and unpolarized neutron diffraction, x-ray diffraction, and density functional theory (DFT) to investigate this transition in single-crystal CaMnBi${}_2$. We observe a coupled structural/magnetic symmetry-lowering transition at $T^{*}=46(2)$~K from a tetragonal lattice with C-type antiferromagnetism to an orthorhombic phase with unit-cell doubling along the $c$ axis, minimal impact on magnetism, and no measurable uniform spin canting ($\lesssim 2^{\circ }$). Superlattice peak intensities and the lattice distortion reveal a continuous second-order transition governed by a single primary order parameter. The refined displacement pattern corresponds to a zigzag bond-order-wave (BOW) modulation of in-plane Bi–Bi bonds, providing direct diffraction evidence for a Peierls-type instability of the Dirac-electron Bi layer anticipated by Hoffmann and co-workers [W.~Tremel and R.~Hoffmann, , 124 (1987); G._A.Papoian and R.~Hoffmann, , 2408 (2000)]. These results identify the $T^{*}$ anomaly as an intrinsic Dirac-electron-driven Peierls/BOW transition of the Bi square net.