The discovery of Ruddlesden-Popper (R-P) nickelate superconductors under high pressure heralds a new chapter of high-transition temperature (high-Tc) superconductivity. Recently, ambient-pressure superconductivity is achieved in R-P bilayer nickelate thin films through epitaxial compressive strain, offering an exceptional platform to investigate the potential symmetry-breaking orders intertwined with high-Tc superconductivity. Here, through electrical transport study, we report an unconventional superconducting phase characterized by time-reversal symmetry (TRS) breaking and electronic glassiness in bilayer nickelate (La, Pr, Sm)3Ni2O7 films. Rather than being inherited from the normal-state instability, this symmetry-broken phase emerges within the superconducting transition regime, and extends to zero-resistance ground state. Three defining characteristics are observed: 1. Magnetoresistance hysteresis, direct evidence of TRS breaking, whose magnetic field-dependence is fundamentally distinct from trapped vortices or long-range-ordered magnetism. Successive oxygen reductions simultaneously weaken both the zero-resistance superconductivity and hysteresis, revealing their intimate correlation . 2. Magnetic field history-dependence and zero-field non-reciprocity in the current-voltage responses, further substantiating the intrinsic and spontaneous TRS breaking. 3. Logarithmically slow resistance relaxations upon the removal of magnetic field, hallmarks of the glassy dynamics. Collectively, our findings uncover an unprecedented superconducting phase in the nickelate superconductors, providing phenomenological and conceptual guidance for future research on high-Tc superconductivity with intertwined symmetry breakings.