We report zero-field-cooled spontaneous-positive and field-cooled conventional-negative exchange bias effects in epitaxial bilayer composed of La0.7Sr0.3MnO3 (LSMO) with ferromagnetic (FM) and Eu0.45Sr0.55MnO3 (ESMO) with A-type antiferromagnetic (AF) heterostructures respectively. A temperature dependent magnetization study of LSMO/ESMO bilayers grown on SrTiO3 (001) manifest FM ordering (TC) of LSMO at ~320 K, charge/orbital ordering of ESMO at ~194 K and AF ordering (TN) of ESMO at ~150 K. The random field Ising model has demonstrated an interesting observation of inverse dependence of exchange bias effect on AF layer thickness due to the competition between FM-AF interface coupling and AF domain wall energy. The isothermally field induced unidirectional exchange anisotropy formed at the interface of FM-LSMO layer and the kinetically phase-arrested magnetic phase obtained from the metamagnetic AF-ESMO layer could be responsible for the spontaneous exchange bias effect. Importantly, no magnetic poling is needed, as necessary for the applications. The FM-AF interface exchange interaction has been ascribed to the AF coupling with [Formula: see text] ([Formula: see text], coupling constant between AF spins) for the spontaneous positive hysteresis loop shift, and the field-cooled conventional exchange bias has been attributed to the ferromagnetically exchanged interface with [Formula: see text] (coupling constant between FM spins).