Floquet dressing offers a route to controlling electronic states through periodic optical driving. Its realization in solids has centred primarily on topological-insulator surface states, semiconductors and two-dimensional Dirac semimetals. Extending this control to bulk metals would enable manipulation of the itinerant states underlying metallic transport and collective order. Yet strong screening and rapid scattering have long cast doubt on its feasibility in bulk metals, while photoelectron dressing complicates its identification. Here we identify Floquet dressing of the overlapping, bulk-derived metallic bands of 2H-NbSe2 using time- and angle-resolved photoemission spectroscopy. Photon-shifted replicas in a sparse unoccupied-state window retain the parent-band dispersions and appear only during pump–probe overlap. Rotating the pump's linear polarization at fixed probe polarization redistributes replica weight between momentum-space branches. With a common parameter set, a model accounting for the optical fields inside and outside the solid captures this redistribution through coherent Floquet–Volkov interference more closely than either pathway alone or their incoherent intensity sum. These findings extend Floquet dressing to the itinerant bulk bands of a multiband metal without relying on the observation of energy gaps opened by hybridization between parent bands and their photon-dressed replicas, providing a basis for exploring how coherent optical dressing couples to metallic transport and collective electronic phases.