We show detail study of asymmetric exchange bias originating from asymmetric behaviour of ascending and descending loops of the magnetic hysteresis of Bi2Fe4O9-BiFeO3 multiferroics nanocomposites. Detail magnetometry study reveals the co-existence of super spin glass (SSG) and dilute antiferromagnet in a field (DAFF) at the interface between antiferromagnetic (AFM) BiFeO3 and ferromagnetic (FM) Bi2Fe4O9 in nanocomposite particles. The interfacial spins behave differently for positive and negative fields and result into asymmetric exchange bias, which has been precisely identified by several critical magnetic measurements such as training effect, stop & wait protocol, isothermal remanence (IRM) & thermoremanence (TRM) measurements, and high field relaxation measurement. The DAFF spins, which generate non-switchable unidirectional anisotropy at the complex FM-SSG-DAFF-AFM interface below Vogel-Fulcher freezing temperature of BiFeO3 at 29.4 K, are solely responsible for such asymmetry in exchange bias.