The emission color from colloidal semiconductor nanocrystals (NCs) is usually tuned through control of particle size, while multicolor emission is obtained by mixing NCs of different sizes within an emissive layer. Here, we demonstrate that recently introduced "dot-in-bulk" (DiB) nanocrystals can emit two-color light under both optical excitation and electrical injection. We show that the effective emission color can be controlled by adjusting the relative amplitudes of the core and shell emission bands via the intensity of optical excitation or applied bias in the cases of photoluminescence (PL) and electroluminescence (EL), respectively. To investigate the role of nonradiative carrier losses due to trapping at intragap states, we incorporate DiB NCs into functional light-emitting diodes and study their PL as a function of applied bias below the EL excitation threshold. We show that voltage-dependent changes in core and shell emissions are not due to the applied electric field but rather arise from the transfer of charges between the anode and the NC intragap trap sites. The changes in the occupancy of trap states can be described in terms of the raising (lowering) of the Fermi level for reverse (direct) bias. We find that the applied voltage affects the overall PL intensity primarily via the electron-trapping channel while bias-induced changes in hole-trapping play a less significant role, limited to a weak effect on core emission.