We report electrical conductance measurements of Bi nanocontacts created by repeated tip-surface indentation using a scanning tunneling microscope at temperatures of 4 K and 300 K. As a function of the elongation of the nanocontact we measure robust, tens of nanometers long plateaus of conductance G0 = 2e^2/h at room temperature. This observation can be accounted for by the mechanical exfoliation of a Bi(111) bilayer, a predicted QSH insulator, in the retracing process following a tip-surface contact. The formation of the bilayer is further supported by the additional observation of conductance steps below G0 before break-up at both temperatures. Our finding provides the first experimental evidence of the possibility of mechanical exfoliation of Bi bilayers, of the existence of the QSH phase in a two-dimensional crystal, and, most importantly, of the observation of the QSH phase at room temperature.