Melt electrospinning is a polymer processing technology for the manufacture of microfibers and nanofibers. Additives are required to reduce the melt viscosity and increase its conductivity in order to minimize the fiber diameter, and can also impart additional beneficial properties. We investigated the preparation of polybutylene succinate (PBS) microfibers incorporating different weight percentages of two multifunctional additives (the organic dye curcumin and inorganic silver nanoparticles) using a single-nozzle laboratory-scale device. We determined the influence of these additives on the polymer melt viscosity, electrical conductivity, degradation profile, thermal behavior, fiber diameter, and antibacterial activity. The formation of a Taylor cone followed by continuous fiber deposition was observed for compounds containing up to 3% (w/w) silver nanoparticles and up to 10% (w/w) curcumin, the latter achieving the minimum average fiber diameter of 12.57 µm. Both additives reduced the viscosity and increased the electrical conductivity of the PBS melt, and also retained their specific antibacterial properties when compounded and spun into fibers. This is the first report describing the effect of curcumin and silver nanoparticles on the properties of PBS fibers manufactured using a single-nozzle melt-electrospinning device. Our results provide the basis to develop environmentally benign antibacterial melt-electrospun PBS fibers for biomedical applications.