Structural analysis of epitaxial layers of the (Ga,Mn)(Bi,As) quaternary dilute magnetic semiconductor (DMS), together with investigations of their magnetotransport properties, has been thoroughly performed. The obtained results are compared with those for the reference (Ga,Mn)As layers, grown under similar conditions, with the aim to reveal an impact of Bi incorporation on the properties of this DMS material. Incorporation of Bi into GaAs strongly enhances the spin-orbit coupling strength in this semiconductor, and the same has been expected for the (Ga,Mn)(Bi,As) alloy. In turn, importantly for specific spintronic applications, strong spin-orbit coupling in ferromagnetic systems opens a possibility of directly controlling the direction of magnetization by the electric current. Our investigations, performed with high-resolution X-ray diffractometry and transmission electron microscopy, demonstrate that the (Ga,Mn)(Bi,As) layers of high structural quality and smooth interfaces can be grown by means of the low-temperature molecular-beam epitaxy method, despite a large difference between the sizes of Bi and As atoms. Depending on the applied buffer layer, the DMS layers can be grown under either compressive or tensile misfit strain, which influences their magnetic properties. It is shown that even small 1% Bi content in the layers strongly affects their magnetoelectric properties, such as the coercive field and anisotropic magnetoresistance.