The phenomenon of exchange bias has been extensively studied within crystalline materials, encompassing a broad spectrum from nanoparticles to thin-film systems. Nonetheless, exchange bias in amorphous alloys has remained a relatively unexplored domain, primarily owing to their inherently uniform disordered atomic structure and lacking grain boundaries. In this study, we present a unique instance of exchange bias observed in Fe-B-Nb amorphous thin films, offering insights into its origins intertwined with the system's spin-glass-like behavior at lower temperatures. The quantification of exchange bias was accomplished through a meticulous analysis of magnetic reversal behaviors in the liquid-helium temperature range, employing a zero-field cooling approach from various initial remanent magnetization states (±MR). At reduced temperatures, the appearance of asymmetric hysteresis, a hallmark of negative exchange bias, undergoes a transformation into symmetric hysteresis loops at elevated temperatures, underscoring the intimate connection between exchange-bias and dynamic magnetic states. Further investigations into the magnetic thermal evolution under varying probe fields reveal the system's transition into a spin-glass-like state at low temperatures. We attribute the origin of this unconventional exchange bias to the intricate exchange interactions within the spin-glass-like regions that manifest at the interfaces among highly disordered Fe-nuclei. The formation of Fe-nuclei agglomerates at the sub-nanometer scale is attributed to the alloy's limited glass-forming ability and the nature of the thin-film fabrication process. We propose that this distinctive form of exchange bias represents a novel characteristic of amorphous thin films.