The photochemical reactions performed by transition metal complexes have been proposed as viable routes towards solar energy conversion and storage into other forms that can be conveniently used in our everyday applications. In order to develop efficient materials, it is necessary to identify, characterize and optimize the elementary steps of the entire process on the atomic scale. To this end, we have studied the photoinduced electronic and structural dynamics in two heterobimetallic ruthenium-cobalt dyads, which belong to the large family of donor-bridge-acceptor systems. Using a combination of ultrafast optical and X-ray absorption spectroscopies, we can clock the light-driven electron transfer processes with element and spin sensitivity. In addition, the changes in local structure around the two metal centers are monitored. These experiments show that the nature of the connecting bridge is decisive for controlling the forward and the backward electron transfer rates, a result supported by quantum chemistry calculations. More generally, this work illustrates how ultrafast optical and X-ray techniques can disentangle the influence of spin, electronic and nuclear factors on the intramolecular electron transfer process. Finally, some implications for further improving the design of bridged sensitizer-catalysts utilizing the presented methodology are outlined.