We study the complex structure of the Bullet cluster radio halo to determine the Dark Matter (DM) contribution to the emission observed in the different subhaloes corresponding to the DM- and baryonic-dominated regions. We use different non-thermal models to study the different regions, and we compare our results with the available observations in the radio, X-ray and gamma-ray bands, and the Sunyaev–Zel'dovich effect (SZE) data. We find that the radio emission coming from the main DM subhalo can be produced by secondary electrons produced by DM annihilations. In this scenario, there are however some open issues, like the difficulty to explain the observed flux at 8.8 GHz, the high value of the required annihilation cross-section, and the lack of observed emission coming from the minor DM subhalo. We also find that part of the radio emission originated by DM annihilation could be associated with a slightly extended radio source present near the main DM subhalo. Regarding the baryonic subhaloes, the radio measurements do not allow to discriminate between a primary or secondary origin of the electrons, while the SZE data point towards a primary origin for the non-thermal electrons in the Main subcluster. We conclude that in order to better constrain the properties of the DM subhaloes, it is important to perform detailed measurements of the radio emission in the regions where the DM haloes have their peaks, and that the separation of the complex radio halo in different subhaloes is a promising technique to understand the properties of each specific subhalo.