A finite element analysis (FEA) driven, automated numerical optimization technique is used to design electric field grading structures in a PCB-integrated bus bar for a 10 kV bondwire-less silicon-carbide (SiC) MOSFET power module. Due to the ultra-high-density of the power module, careful design of field-grading structures inside the bus bar is required to mitigate the high electric field strength in the air. Using Bayesian optimization and a new weighted point-of-interest (POI) cost function, the highly non-uniform electric field is efficiently optimized without the use of field integration, or finite-difference derivatives. The proposed optimization technique is used to efficiently characterize the performance of the embedded field grading structure, providing insights into the fundamental limitations of the system. The characterization results are used to streamline the design and optimization of the bus bar and high-density module interface. The high-density interface experimentally demonstrated a partial discharge inception voltage (PDIV) of 11.6 kV rms. When compared to a state-of-the-art descent-based optimization technique, the proposed algorithm converges 3x faster and with 7x smaller error, making both the field grading structure and the design technique widely applicable to other high-density high-voltage design problems.