  The current dependence of the excess conductivity is measured up to $\simeq 3
T_c$ for a Bi$_2$Sr$_2$CuO$_{6+\delta}$ thin film, as a function of doping. It
is found to be anomalously sensitive to the transport current and to behave as
a universal function of $T/T_c$ in the whole doping range. We discuss these
results in the perspective of a granular superconductor with a gapless-like
behavior.
