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Harnessing extra degrees of freedom in magnetic oxides is of vital importance to bring new functionalities to cooling technology. The present study reports on the magnetocaloric effect (MCE) and magnetic exchange bias effect in the SrRuO$_{3}$ single layer and BiFeO$_{3}$/SrRuO$_{3}$ bilayers. MCE and exchange bias behaviors are found to be governed by Ru vacancies, structural distortions, and interfacial inter-diffusions. Additionally, the MCE is simulated using Maxwell's equations from both in-plane and out-of-plane magnetization data. The maximum entropy change ($|\Delta S|$) of 120 mJ/kg$\cdot$K and adiabatic temperature change ($\Delta T_{ad}$) of 0.028 K at a small field of 0.01 T are observed around the Curie temperatures ($T_{C}$) of SrRuO$_{3}$ layer in the out-of-plane directions. The variation in the maximum $|\Delta S|$ (70-120 mJ/kg$\cdot$K) and corresponding $T_{C}$ values (138-100 K) reveal that Ru vacancies can significantly contribute to tuning the MCE. Interestingly, BiFeO$_{3}$/SrRuO$_{3}$ bilayer structures are found to sustain not only MCE over a broad temperature range with different $\Delta S$ peaks but also exhibit a huge coercivity enhancement, making them attractive for improved on-chip cooling and spintronic devices.