Bi0.98Na0.02Fe1-xRuxO3 (x = 0, 0.01, 0.02) samples were prepared via a sol-gel method. The formation of the desired materials was confirmed using X-ray diffraction. The tetravalent Ru doping could effectively reduce the number of oxygen vacancy, and subsequently reduce the leakage current. Interestingly, the optical band gap was narrowed gradually in our samples, which seems contradictory with the variation in oxygen vacancy. To better understand this abnormal optical property, the effect of bandwidth was analyzed based on the change in Fe-O bond length and Fe-O-Fe bond angle, and the corresponding phenomenological qualitative model was proposed. The magnetization was increased with Ru substitution. In addition, an exchange bias (EB) phenomenon without field cooled process was observed at room temperature for all the samples, which was explained by introducing a core-shell structure model. Moreover, the EB behavior becomes more pronounced at 5 K for 1% Ru-doped sample.