Bulk Rashba systems BiTeX (X = I, Br, Cl) are emerging as important candidates for developing spintronics devices because of the coexistence of spin-split bulk and surface states, along with the ambipolar character of the surface charge carriers. The need to study the spin texture of strongly spin-orbit-coupled materials has recently promoted circular dichroic angular resolved photoelectron spectroscopy (CD-ARPES) as an indirect tool to measure the spin and the angular degrees of freedom. Here we report a detailed photon-energy-dependent study of the CD-ARPES spectra in BiTeX (X = I, Br, Cl). Our work reveals a large variation in the magnitude and sign of the dichroism. Interestingly, we find that the dichroic signal modulates differently for the three compounds and for the different spin-split states. These findings show a momentum and photon-energy dependence for the CD-ARPES signals in the bulk Rashba semiconductor BiTeX (X = I, Br, Cl). Finally, the outcome of our experiment indicates the important relation between the modulation of the dichroism and the phase differences between the wave functions involved in the photoemission process. This phase difference can be due to initial- or final-state effects. In the former case the phase difference results in possible interference effects among the photoelectrons emitted from different atomic layers and characterized by entangled spin-orbital polarized bands. In the latter case the phase difference results from the relative phases of the expansion of the final state in different outgoing partial waves.