In the present work, the thermal convective instability of hybrid bi-viscous Bingham nanofluid is numerically investigated using the Chebyshev spectral method. Considering the importance of gold and iron oxide nanoparticles in medical fields for optimized and targeted drug delivery, blood suspended with gold and iron oxide nanoparticles is taken as the working fluid. Flow dynamics are modeled using the modified Brinkman model for hybrid fluid and bi-viscous Bingham fluid model under the effect of Brownian, thermophoretic diffusion, and internal heat generation. The eigenvalue problem is derived from the linear stability analysis and normal mode technique. Further, the resulting eigenvalue problem is solved using the Chebyshev spectral method. The effect of pertinent flow governing parameters on the threshold of onset of convection is graphically presented and discussed in detail. It is observed that bi-viscous Bingham fluid suspended with only iron oxide nanoparticles is highly stable in the absence of an internal heat source.