We report the composition-dependent optical properties of Bi-doped Cs2Ag1-xNaxInCl6 nanocrystals (NCs) having a double perovskite crystal structure. Their photoluminescence (PL) was characterized by a large Stokes shift, and the PL quantum yield increased with the amount of Na up to ∼22% for the Cs2Ag0.4Na0.6InCl6 stoichiometry. The presence of Bi3+ dopants was crucial to achieve high PL quantum yields (PLQYs) as nondoped NC systems were not emissive. Density functional theory calculations revealed that the substitution of Ag+ with Na+ leads to localization of AgCl6 energy levels above the valence band maximum, whereas doping with Bi3+ creates BiCl6 states below the conduction band minimum. As such, the PL emission stems from trapped emission between states localized in the BiCl6 and AgCl6 octahedra, respectively. Our findings indicated that both the partial replacement of Ag+ with Na+ ions and doping with Bi3+ cations are essential in order to optimize the PL emission of these systems.