Osmium-containing oxides are rare due to the difficulty in stabilizing complex structures with a fixed stoichiometry and metastability of the phases. Bismuth-substituted thallium osmate pyrochlore samples, Tl2-xBixOs2O7-y, were synthesized using solid-state reactions where the solubility limit was found to be approximately x = 1.4. Members of this solid solution were characterized by their structural, electronic, magnetic, and thermal properties to understand the influence of Bi3+ substitution on the ground state. The Os-containing pyrochlores crystallize in the ideal cubic pyrochlore structure (Fd (3) over barm), and the lattice parameter a was found to slightly increase as a function of Bi content. A possible interplay between structure and cation valence states was explored using both neutron powder diffraction and X-ray absorption spectroscopy, suggesting that a combination of Os4+/Os5+ and Tl1+/Tl3+ mixed valency throughout the solid solution allows for the stabilization of the pyrochlore structure. The system is metallic for the entire solid solution and predominantly exhibits temperature-independent paramagnetism. Specific heat measurements show an enhanced Sommerfeld coefficient, a possible flat-band signature. This system gave insight into the bonding preferences of Os, indicating a dependence on high oxidation states and mixed valence for the stability of complex structures.