  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). 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. 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" 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 x
10^14 solar mass within a 250 kpc radial aperture.
