There is a wealth of data on live, undecayed 60Fe (t1/2 = 2.6 Myr) in deep-sea deposits, the lunar regolith, cosmic rays, and Antarctic snow, which is interpreted as originating from the recent explosions of at least two near-Earth supernovae. We use the 60Fe profiles in deep-sea sediments to estimate the timescale of supernova debris deposition beginning ∼3 Myr ago. The available data admits a variety of different profile functions, but in all cases the best-fit 60Fe pulse durations are >1.6 Myr when all the data is combined. This timescale far exceeds the ≲0.1 Myr pulse that would be expected if 60Fe was entrained in the supernova blast wave plasma. We interpret the long signal duration as evidence that 60Fe arrives in the form of supernova dust, whose dynamics are separate from but coupled to the evolution of the blast plasma. In this framework, the >1.6 Myr is that for dust stopping due to drag forces. This scenario is consistent with the simulations in Fry et al. (2020), where the dust is magnetically trapped in supernova remnants and thereby confined around regions of the remnant dominated by supernova ejects, where magnetic fields are low. This picture fits naturally with models of cosmic-ray injection of refractory elements as sputtered supernova dust grains and implies that the recent 60Fe detections in cosmic rays complement the fragments of grains that survived to arrive on the Earth and Moon. Finally, we present possible tests for this scenario.