Ferromagnetic semiconductor thin layers of the quaternary (Ga,Mn)(Bi,As) and reference, ternary (Ga,Mn)As compounds, epitaxially grown under either compressive or tensile strain, have been characterized from a perspective of structural and magnetization homogeneity. The quality and composition of the layers have been confirmed by secondary-ion mass spectrometry (SIMS). A thorough evaluation of the magnetic properties as a function of temperature and applied magnetic field has been performed by means of SQUID magnetometry and low-energy muon spin relaxation (μSR) spectroscopy, which enables studying local (on the nanometer scale) magnetic properties of the layers. The results testify that the ferromagnetic order builds up almost homogeneously below the Curie temperature in the full volume fraction of both the (Ga,Mn)As and (Ga,Mn)(Bi,As) layers. Incorporation of a small amount of heavy Bi atoms into (Ga,Mn)As, which distinctly enhances the strength of spin-orbit coupling in the quaternary (Ga,Mn)(Bi,As) layers, does not deteriorate noticeably their magnetic properties.