Coupling at the interface of core/shell magnetic nanoparticles is known to be responsible for exchange bias (EB) and the relative sizes of core and shell components are supposed to influence the associated phenomenology. In this work, we have prepared core/shell structured nanoparticles with a total average diameter around ∼27 nm and a wide range of shell thicknesses through the controlled oxidation of Co nanoparticles well dispersed in an amorphous silica host. Structural characterizations give compelling evidence of the formation of Co3O4 crystallite phase at the shells surrounding the Co core. Field cooled hysteresis loops display nonmonotonous dependence of the exchange bias HE and coercive HC fields, that become maximum for a sample with an intermediate shell thickness, at which lattice strain is also maximum for both phases. The EB effects persist up to temperatures above the ordering temperature of the oxide shell. Results of our atomistic Monte Carlo simulations of particles with the same size and composition as in experiments are in agreement with the experimental observations and have allowed us to identify a change in the contribution of the interfacial surface spins to the magnetization reversal, giving rise to the observed maximum in HE and HC.