With the addition of additives, lubricating fluid begins to behave non-linearly. Besides that, the emergence of ultra-high-speed machines with highly polished surfaces causes slip between the sliding surfaces, violating the no-slip boundary condition. The current novel research work looks at the performance of the bearing while considering the combined effect of the non-Newtonian and wall-slip impact of the lubricant. Furthermore, the model developed can account for the influences of slip-lengths acting in orthogonal directions at the solid-fluid interface of both sliding surfaces. This innovative model produces more realistic steady-state and dynamic performance results than the classic Reynolds hypothesis. The FDM is employed to determine the pressure developed using the SOR approach. The findings divulge that the occurrence of wall-slip on the journal surface significantly impacts bearing performance. The journal center trajectories that determine the system's stability are estimated using non-linear transient analysis. The findings reveal that, at a power-law index of 0.75 and slip-length of 0.2, dimensionless pressure increases by 10%, resulting in higher load-carrying capacity. The flow rate is increased by 6.5%, and above all, the stability region has grown by about 19.45%.