High-quality single crystals of perovskite-like (CH₃NH₃)₃Bi₂I₉ hybrids have been synthesized, using a layered-solution crystal-growth technique. The large dielectric constant is strongly affected by the polar ordering of its constituents. Progressive dipolar ordering of the methylammonium cation upon cooling below 300 K gradually converts the hexagonal structure (space group P6₃/mmc) into a monoclinic phase (C2/c) at 160 K. A well-pronounced, ferrielectric phase transition at 143 K is governed by in-plane ordering of the bismuth lone pair that breaks inversion symmetry and results in a polar phase (space group P2₁). The dielectric constant is markedly higher in the C2/c phase above this transition. Here, the bismuth lone pair is disordered in-plane, allowing the polarizability to be substantially enhanced. Density functional theory calculations estimate a large ferroelectric polarization of 7.94 μC/cm² along the polar axis in the P2₁ phase. The calculated polarization has almost equal contributions of the methylammonium and Bi³⁺ lone pair, which are fairly decoupled.