Electronic transport properties of bismuth nanocontacts are analyzed using a low temperature scanning tunneling microscope. The subquantum steps observed in the conductance versus elongation curves give evidence of atomic rearrangements in the contact. The quantum nature of the conductance reveals itself through peaks in the conductance histograms. The shape of the curves at 77 K is described by a simple gliding mechanism for the contact evolution during elongation. The different behavior at 4 K suggests a transition from light to heavy charge carriers as the contact cross section is decreased.