We report a combined infrared and angle-resolved photoemission study of the electronic response of Sr-3(Ir-1_Ru-x(x))(2)O-7 (x = 0, 0.22, 0.34). The low-temperature optical conductivities of the three compounds exhibit the characteristic feature of the effective total angular momentum J(eff) =1/2 antiferromagnetic Mott state. As the temperature increases across the antiferromagnetic ordering temperature T-N, the indirect gap gradually closes whereas the direct gap remains open. In the optical conductivity of Sr-3(Ir0.66Ru0.34)(2)O-7 which shows a thermally driven insulator-metal transition at T-N, a Drude-like response from itinerant carriers is registered in the paramagnetic phase. We observe in angle-resolved photoemission data of Sr-3(Ir0.66Ru0.34)(2)O-7 that the valence band shifts continuously toward the Fermi energy with the weakening of the antiferromagnetic order and crosses the Fermi level in the paramagnetic phase. Our findings demonstrate that the temperature-induced metal-insulator transition of the Sr-3(Ir-1_Ru-x(x))(2)O-7 system should be attributed to a magnetically driven band shift.