The heat dissipation factor of conventional epoxy impregnated paper bushings is a subject of concern due to the large quantities of power in a High Voltage Direct Current (HVDC) system. The present work deals with the selection of better insulation as a replacement to the conventional resin impregnated material employing nano-hexagonal-Boron Nitride and nano-hexagonal-Boron Nitride added with nano-cellulose-fiber. The bushing of the converter transformer is designed using the Finite Element Method (FEM), and the electrothermal analysis is performed at the loaded working condition. Besides, numerous optimization schemes are also presented for adapting the structure of the thermal conductor enclosed in the inner conductor. The electrothermal performances of the above materials with the optimized structure are compared and an advanced scheme is proposed. Further, the results obtained from the designed system are employed in the form of an Artificial Neural Network to simplify the process of thermal computation characterized by the selected scheme. The internal parameters of the neural network are tuned implementing a hybrid amalgamation of Particle Swarm optimization - Grey Wolf Optimiser and the performance is compared against the actual values. The supremacy of the implemented algorithm is justified by a comparative analysis with other well-established algorithms using various statistical parameters.