This study explores an eco-friendly method for recovering platinum group metals from a synthetic automotive three-way catalyst (TWC). Bioleaching of palladium (Pd) using the thiosulfate-copper-ammonia leaching processes, with biogenic thiosulfate sourced from a bioreactor used for biogas biodesulfurization, is proposed as a sustainable alternative to conventional methods. Biogenic thiosulfate production was optimized in a gas-lift bioreactor by studying the pH (8–10) and operation modes (batch and continuous) under anoxic and microaerobic conditions for 35 d. The maximum concentration of 4.9 g S2O32− L−1 of biogenic thiosulfate was reached under optimal conditions (batch mode, pH = 10, and airflow rate 0.033 vvm). To optimize Pd bioleaching from a ground TWC, screening through a Plackett–Burman design determined that oxygen and temperature significantly affected the leaching yield negatively and positively, respectively. Based on these results, an optimization through an experimental design was performed, indicating the optimal conditions to be Na2S2O3 1.2 M, CuSO4 0.03 M, (NH4)2SO4 1.5 M, Na2SO3 0.2 M, pH 8, and 60 °C. A remarkable 96.2 and 93.2% of the total Pd was successfully extracted from the solid at 5% pulp density using both commercially available and biogenic thiosulfate, highlighting the method’s versatility for Pd bioleaching from both thiosulfate sources.