The recent discovery of high-temperature superconductivity in the bilayer nickelate La₃Ni₂O₇ has led to extensive interest in the correlation physics of its normal state. Given that the superconducitivity develops near a density wave order in the phase diagram, it is important to elucidate the nature of this order. Based on the accumulated experimental evidence for a bad metal state in proximity to an orbital-selective Mott phase, here we describe magnetic correlations of the system in a conceptually new way – in terms of effective local moments experiencing a combination of RKKY and superexchange interactions. This gives rise to a magnetic order with a wavevector that is close to Q=(π/2,π/2) and, at the same time, yields a clear understanding of the associated spin dynamics. Our results are consistent with the rapidly emerging experiments about the magnetic correlations in the density wave order of the bilayer nickelate. Implications for unconventional superconductivity in this and related multiorbital systems are discussed.