Superconductivity that spontaneously breaks time-reversal symmetry (TRS) has been found, so far, only in a handful of three-dimensional (3D) crystals with bulk inversion symmetry. We report an observation of spontaneous TRS breaking in a 2D superconducting system without inversion symmetry: the epitaxial bilayer films of bismuth and nickel. The evidence comes from the onset of the polar Kerr effect at the superconducting transition in the absence of an external magnetic field, detected by the ultrasensitive loop-less fiber-optic Sagnac interferometer. Because of strong spin-orbit interaction and lack of inversion symmetry in a Bi/Ni bilayer, superconducting pairing cannot be classified as singlet or triplet. We propose a theoretical model where magnetic fluctuations in Ni induce the superconducting pairing of the d(xy) +/- id(x)(2)-(2)(y) orbital symmetry between the electrons in Bi. In this model, the order parameter spontaneously breaks the TRS and has a nonzero phase winding number around the Fermi surface, thus making it a rare example of a 2D topological superconductor.