Aims. We present a new strong lensing mass reconstruction of the Bullet cluster (1E 0657-56) at z = 0 : 296, based on WFC3 and ACS HST imaging and VLT/FORS2 spectroscopy. The strong lensing constraints underwent substantial revision compared to previously published analysis, there are now 14 (six new and eight previously known) multiply-imaged systems, of which three have spectroscopically confirmed redshifts (including one newly measured from this work). Methods. The reconstructed mass distribution explicitly included the combination of three mass components: (i) the intra-cluster gas mass derived from X-ray observation; (ii) the cluster galaxies modeled by their fundamental plane scaling relations and (iii) dark matter. Results. The model that includes the intra-cluster gas is the one with the best Bayesian evidence. This model has a total rms value of 0 : 158 0 0 between the predicted and measured image positions for the 14 multiple images considered. The proximity of the total rms to resolution of HST/WFC3 and ACS (0.07 0.15" FWHM) demonstrates the excellent precision of our mass model. The derived mass model confirms the spatial offset between the X-ray gas and dark matter peaks. The fraction of the galaxy halos mass to total mass is found to be f(s) = 11 +/- 5% for a total mass of 2 : 5 +/- 0 : 1 +/- 10(14) M-circle dot within a 250 kpc radial aperture.