The analysis of the cluster environment is a valuable instrument to investigate the origin of AGN and star-forming galaxies gas fuelling and trigger mechanisms. To this purpose, we present a detailed analysis of the point-like X-ray sources in the Bullet cluster field. Thanks to $sim600$ ks Chandra observations, we produced a catalogue of 381 X-ray point sources up to a distance of $sim$1.5 virial radius and with flux limits $sim1times10^{-16}$ and $sim8times10^{-16}$ erg cm$^{-2}$ s$^{-1}$ in the 0.5-2 keV and 2-10 keV bands, respectively. We found a strong (up to a factor 1.5-2) and significant ($ge$4$sigma$) over-density in the full region studied $0.3R_{200}<R<1.5R_{200}$. We identified optical and infrared counterparts for $sim$84% and $sim$48% of the X-ray sources, respectively. We obtained new spectroscopic redshifts for 106 X-ray sources. Spectroscopic and photometric redshifts of optical and infrared sources have been also collected, and these sources were used as ancillary samples. We find that the over-density in the region $0.3R_{200}<R<R_{200}$ is likely due to X-ray AGN (mostly obscured) and star-forming galaxies both associated to the cluster, while in the more external region it is likely mostly due to background AGN. The fraction of cluster galaxies hosting an X-ray detected AGN is 1.0$pm$0.4$%$, nearly constant with the radius, a fraction similar to that reported in other clusters of galaxies at similar redshift. The fraction of X-ray bright AGN (L$_{2-10keV}$$>$10$^{43}$ ergs s$^{-1}$) in the region $0.3R_{200}<R<R_{200}$ is $0.5^{+0.6}_{-0.2}$$%$, higher than that in other clusters at similar redshift and more similar to the AGN fraction in the field. Finally, the spatial distributions of AGN and star-forming galaxies, selected also thanks to their infrared emission, appear similar, thus suggesting that both are triggered by the same mechanism.
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