We present data of transport measurements through a metallic nanobridge exhibiting diffusive electron transport. A logarithmic temperature dependence and a zero-bias anomaly in the differential conductance are observed, independent of magnetic field. The data can be described by a single scaling law. The theory of electron-electron interaction in disordered systems, adapted to the case of finite-size systems in non-equilibrium, yields quantitative agreement with experiment. Measurements of universal conductance functuations support the assumptions of the theory about the electronic phase coherence.