Antibacterial properties of engineered materials are important in the transition to a circular economy and societal security, as they are central to many key industrial areas, such as health, food, and water treatment/reclaiming. Nanocoating and electrospinning are two versatile, simple, and low-cost technologies that can be combined into new advanced manufacturing approaches to achieve controlled production of innovative micro- and nano-structured non-woven membranes with antifouling and antibacterial properties. The present study investigates a rational approach to design and manufacture electrospun membranes of polysulfone (PSU) with mechanical properties optimized via combinatorial testing from factorial design of experiments (DOE) and endowed with antimicrobial silver (Ag) nanocoating. Despite the very low amount of Ag deposited as a conformal percolating nanocoating web on the polymer fibers, the antimicrobial resistance assessed against the Gram-negative bacteria E. coli proved to be extremely effective, almost completely inhibiting the microbial proliferation with respect to the reference uncoated PSU membrane. The results are relevant, for example, to improve antifouling behavior in ultrafiltration and reverse osmosis in water treatment.