We have observed conventional signatures of exchange bias (EB), in the form of a shift in the field-cooled hysteresis loop, and a training effect, in BiFe0.8Mn0.2O3 nanoparticles. From neutron diffraction, thermoremanent magnetization, and isothermoremanent magnetization measurements, the nanoparticles are found to be core shell in nature, consisting of an anti ferromagnetic (AFM) core, and a two-dimensional diluted AFM (DAFF) shell with a net magnetization under a field. The analysis of the training effect data using Binek’s model shows that the observed loop shift arises entirely due to an interface exchange coupling between the core and shell, and the intrinsic contribution of the DAFF shell to the total loop shift is zero. A significantly high value of the EB field has been observed at room temperature. The present study is useful to understand the origin of EB in other DAFF-based systems as well.