The structure and composition of single GaAsBi/GaAs epilayers grown by molecular beam epitaxy were investigated by optical and transmission electron microscopy techniques. Firstly, the GaAsBi layers exhibit two distinct regions and a varying Bi composition profile in the growth direction. In the lower (25 nm) region, the Bi content decays exponentially from an initial maximum value, while the upper region comprises an almost constant Bi content until the end of the layer. Secondly, despite the relatively low Bi content, CuPtB-type ordering was observed both in electron diffraction patterns and in fast Fourier transform reconstructions from high-resolution transmission electron microscopy images. The estimation of the long-range ordering parameter and the development of ordering maps by using geometrical phase algorithms indicate a direct connection between the solubility of Bi and the amount of ordering. The occurrence of both phase separation and atomic ordering has a significant effect on the optical properties of these layers. PACS: 78.55.Cr III-V semiconductors; 68.55.Nq composition and phase identification; 68.55.Ln defects and impurities: doping, implantation, distribution, concentration, etc; 64.75.St phase separation and segregation in.