The current research designed a statistical model for the bobbin tool friction stir processing (BT-FSP) of AA1050 aluminum alloy using the Response Surface Method (RSM). The analysis studied the influence of tool travel speeds of 100, 200, and 300 mm/min and different pin geometries (triangle, square, and cylindrical) at a constant tool rotation speed (RS) of 600 rpm on processing 8 mm thickness AA1050. The developed mathematical model optimizes the effect of the applied BT-FSP parameters on machine torque, processing zone (PZ) temperature, surface roughness, hardness values, and ultimate tensile strength (UTS). The experimental design is based on the Face Central Composite Design (FCCD), using linear and quadratic polynomial equations to develop the mathematical models. The results show that the proposed model adequately predicts the responses within the processing parameters, and the pin geometry is the most influential parameter during the BT-FSP of AA1050. The analysis of variance exhibit that the developed mathematical models can effectively predict the values of the machine torque, PZ temperature, surface roughness, hardness, and UTS with a confidence level of over 95% for the AA1050 BT-FSP. The optimization process shows that the optimum parameters to attain the highest mechanical properties in terms of hardness and tensile strength at the lowest surface roughness and machine torque are travel speed (TS) of 200 mm/min using cylindrical (Cy) pin geometry at the constant RS of 600 rpm. The PZ temperature of the processed specimens decreased with increasing TS at different pin geometries. Meanwhile, the surface roughness of the processed passes and machine torque increased with increasing the TS at different pin geometries. Increasing TS from 100 to 300 mm/min increases the hardness values of the processed materials using different pin geometries. The highest UTS of 79 MPa for the processed specimens was attained at the TS of 200 mm/min and RS of 600 rpm using the Cy pin geometry.