Fibers with diameters in the lower micrometer range have unique properties suitable for applications in the textile and biomedical industries. Such fibers are usually produced by solution electrospinning, but this process is environmentally harmful because it requires the use of toxic solvents. Melt electrospinning is a sustainable alternative but the high viscosity and low electrical conductivity of molten polymers produce thicker fibers. Here, we used multifunctional biobased dyes as additives to improve the spinnability of polylactic acid (PLA), improving the spinnability by reducing the electrical resistance of the melt, and incorporating antibacterial activity against Staphylococcus aureus. Spinning trials using our 600-nozzle pilot-scale melt-electrospinning device showed that the addition of dyes produced narrower fibers in the resulting fiber web, with a minimum diameter of ~9 µm for the fiber containing 3% (w/w) of curcumin. The reduction in diameter was low at lower throughputs but more significant at higher throughputs, where the diameter reduced from 46 µm to approximately 23 µm. Although all three dyes showed antibacterial activity, only the PLA melt containing 5% (w/w) curcumin retained this property in the fiber web. Our results provide the basis for the development of environmentally friendly melt-electrospinning processes for the pilot-scale manufacturing of microfibers.