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There is much interest in SmB₆ as a potential topological insulator, owing to the robustness of its bulk insulating state originating from the Kondo effect. We have carried out a muon spin rotation (μSR) study of the μ⁺-Knight shift in SmB₆. Our measurements probe bulk rather than surface properties. At low temperatures where Kondo hybridization is complete and at magnetic fields far below what is necessary to close the insulating gap, we observe a magnetic dipolar shift that is indicative of a partially Kondo-compensated Sm moment sublattice. Concomitantly, we detect a contact hyperfine field at the muon site that seems to arise from a direct overlap with the wavefunction of delocalized magnetic Sm-4f electrons. This contact hyperfine field and hence degree of 4f-electron delocalization is strongly reduced below 6 K, where metallic surface states dominate electrical transport. Our results support a ground state in which the insulating bulk is somewhat fragile and on the verge of supporting magnetic order.