Electron transfers (ET) between a donor (D) and an acceptor (A) through a molecular bridge (B) are of great importance in biological systems, molecular electronics and molecular based light-energy conversion systems. Here, the back and the forward electron transfer rates have been measured by femtosecond and nanosecond spectroscopy in a heterogeneous donor-bridge-acceptor (D-B-A) system, where D = ruthenium terpyridine complex, B = p-oligo(phenylene) and A = TiO(2). The forward ET rate (from 0.85 to 3.7 ps(-1)) is faster than the nonequilibrium vibrations relaxation rate of the hot (3)MLCT (metal-to-ligand charge transfer) state of the donor (12 ps(-1) in solution). The back ET occurs on the microsecond time scale. Regarding the distance dependence behaviour, damping factors 0.16 and 0.47 angstrom(-1) of the forward and the back ET respectively are obtained. These results confirm that the damping factor is not only linked to the nature of the molecular bridge but to the full D-B-A system. This unusual low damping factor observed for the forward ET is attributed to a decrease of the tunnelling energy gap Delta E, which is induced by the nonequilibrium vibrations at the donor-bridge interface. This enhanced electron transmission is briefly discussed within the concept of a nonequilibrium polaron relaxation towards the dissipative acceptor. In this case, the dissipation of the excess vibrational energy and the electron transfer occur in a synchronized cooperative way.