In this work the measurements of longitudinal (LMR) and transverse magnetoresistance (TMR) in Bi wires with 50<d<500 nm in the interval 4.2 - 300 K and magnetic field up to 14 T were carried out. Was shown that, the maximum on LMR at H∥I is suppressed due to quantum size effect. For the first time it was found that the field dependence of TMR R(H) at I⊥H) in Bi wires with d<80 nm contains the negative region R(H) > R₀ at T<5 K. This result was unexpected, because it is known that in bulk Bi samples the "giant" increase of magnetoresistance in the case H⊥I is observed. We calculate the conductivity of nanowires in longitudinal and transverse magnetic fields on the basis of the Cubo formula for the conductivity. We use the model of quantum wires with a parabolic potential in the plane orthogonal to the axis of the size-quantized system. According to the model of such TMR and LMR were experimentally observed in the Bi quantum wires (QW) with d<80nm.