We studied the structural and physical properties of the hypervalent system Ba₂Bi(Sb_1−xBi_x)2 (0 ≤ x ≤ 1) with an anisotropic “square–honeycomb” layer. We found that the orthorhombic Ba₂BiSb₂ (x = 0) shows a charge density wave (CDW) transition at approximately 230 K accompanied by a significant elongation of the b-axis, indicating the quasi-one-dimensional nature along the b-axis in its electronic state, as supported by first-principles calculations. This CDW transition is rapidly suppressed with increasing x, leading to the appearance of superconductivity for 0.375 ≤ x ≤ 1. The superconducting transition temperature T_c increases slightly with x and the maximum T_c was 4.4 K for Ba₂Bi₃ (x = 1).