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Superconductivity that spontaneously breaks time-reversal symmetry (TRS) has been found, so far, only in a handful of 3D crystals with bulk inversion symmetry. Here 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 superconducting pairing of the d_{xy} +- id_{x^2-y^2} orbital symmetry between the electrons in Bi. This order parameter spontaneously breaks the TRS and has a non-zero phase winding number around the Fermi surface, thus making Bi/Ni a rare example of a 2D topological superconductor.