In this work, we have studied mixed III-V semiconductors of the Al(As, Bi) composition. We have examined a number of ordered structures of this composition in a series of first-principles calculations within the density functional theory, making use of full-potential linearized augmented plane-wave method, as implemented in the WIEN2k code. The calculations have been done for ``minimal'' super-cells realizing the 1: 3, 1: 1, and 3: 1 relations of As: Bi at the anion sublattice. Specifically, the CuAu and chalcopyrite structures were considered for the 1: 1 relation; the famatinite and luzonite structures for the 1:3. In all cases, the full structure optimization has been performed with spineorbit interaction taken into account, and the band structure/band gap analysis done. As expected, an insertion of Bi into the AlAs enlarges, on the average, the cell volume and results in marked disparity of the bond lengths. The optical band gap decreases with Bi composition; the indirect to direct band gap crossover is interpolated to happen at nearly 16% of Bi. The spineorbit splitting increases with Bi compositions, and exceeds the band gap starting from Bi composition of about 50%. The study is concluded by a report on calculated optical properties, i.e., the dielectric function and refractive index, for different Bi compositions.