We observed for the first time the effect of the negative magnetoresistance (NMR) in transverse magnetic fields (B ⊥ I) in quantum Bi wires at 4.2 K; this effect is described in this work. The single crystal bismuth wires in a glass cover were produced using the liquid phase casting methods. The Bi wires are strictly cylindrical with the (1011) orientation along the wire axis and diameters ranging from 50 to 400 nm. In wires with a diameter of d < 80 nm, there was observed a semimetal-semiconductor transition, which is associated with the quantum size effect and is attended with a “semiconductor” temperature dependence of the resistance R(T). In weak transverse magnetic fields, there was observed an NMR effect both at B ‖ C₂ and at B ‖ C₃. The increase in the wire diameter d, temperature T, and magnetic field B results in the weakening and total disappearance of the found peculiarities of NMR in weak magnetic fields, thus reflecting the suppression of the size quantization effect. An analytical simulation of the quantum wire that makes it possible to explain the nonmonotonic character of the transverse magnetoresistance in Bi wires is considered. To interpret this NMR effect, we have used a theoretical model in which the electrical conductivity is calculated using the Cubo formula with account for the elastic scattering of the carriers on phonons and the size quantization of the energy spectrum. The comparison of the experimental results with the analytic model allows us to conclude that the observed NMR effect in the transverse magnetic field in Bi nanowires has a quantum nature.