Three-dimensional topological ferroelectric (3D-TFE) insulators, in which topological and ferroelectric orders naturally coexist, enable field-controlled spintronic devices. In this work, we predict a previously unknown structure of bismuth monohalides Bi${}_4{X}_4$ ($X$ = Br, I), denoted the $\gamma$ phase, and demonstrate that it is an ideal 3D-TFE insulator. Systematic first-principles calculations confirm the stability and synthesizability of $\gamma$-Bi${}_4{X}_4$. Although the noncentrosymmetric $\gamma$ phase crystallizes in the space group $Cmc{2}_1$ with no symmetry-based classifications/indicators, the nontrivial topology can be characterized by the nonzero spin Chern number. Moreover, the $z$-direction polarization can be switched by interlayer sliding with a small energy barrier. Finally, we design an electrically controlled spin-filter device that can generate a switchable spin-polarized current. Combining a single-phase crystal, a sizable band gap, and robust band topology against FE switching, these bismuth monohalides serve as a prototype of intrinsic 3D-TFE insulators, providing an ideal platform for realizing new nonvolatile functionalities in spintronic devices.