We present high-resolution conductance measurements in niobium nanowires below the superconducting transition temperature. During elongation we find a bistability region manifesting itself as random telegraph noise. Density functional structural optimizations and conductance calculations reproduce and explain the measurements. In particular, the observed bistability is associated with the formation of a niobium dimer between the opposing electrodes, with the dimer shuttling between a symmetric, high conductance, and an asymmetric, low-conductance configurations in the gap.