We investigate the superconducting gap structure in bilayer nickelates within a model where conduction bands of d_x2-y2 symmetry coexist with localized d_3z2-r2 spins. Strong interlayer coupling drives the local moments into a singlet ground state, whose virtual singlet–triplet excitations (“triplons”) mediate the pairing interaction between conduction electrons. This yields interband s _± pairing, with opposite signs of the order parameter on the two (α and β) bands. Our theory naturally explains the key experimental features: a larger gap on the α band despite its smaller density of states, and pronounced gap anisotropy arising from nonlocal Kondo coupling. The results support triplon-mediated pairing as the microscopic origin of superconductivity in bilayer nickelates.