We present observations of the Sunyaev-Zel ’ dovich effect ( SZE ) in the Bullet cluster ( 1E 0657–56 ) using the APEX-SZ instrument at 150 GHz with a resolution of 1 \arcmin . The main results are maps of the SZE in this massive , merging galaxy cluster . The cluster is detected with 23 \sigma significance within the central 1′ radius of the source position . The SZE map has a broadly similar morphology to that in existing X-ray maps of this system , and we find no evidence for significant contamination of the SZE emission by radio or IR sources . In order to make simple quantitative comparisons with cluster gas models derived from X-ray observations , we fit our data to an isothermal elliptical \beta model , despite the inadequacy of such a model for this complex merging system . With an X-ray derived prior on the power-law index , \beta = 1.04 ^ { +0.16 } _ { -0.10 } , we find a core radius r _ { c } = 142 \pm 18 \arcsec , an axial ratio of 0.889 \pm 0.072 , and a central temperature decrement of -771 \pm 71 \mu { K _ { CMB } } , including a \pm 5.5 \% flux calibration uncertainty . Combining the APEX-SZ map with a map of projected electron surface density from Chandra X-ray observations , we determine the mass-weighted temperature of the cluster gas to be T _ { mg } = 10.8 \pm 0.9 keV , significantly lower than some previously reported X-ray spectroscopic temperatures . Under the assumption of an isothermal cluster gas distribution in hydrostatic equilibrium , we compute the gas mass fraction for prolate and oblate spheroidal geometries and find it to be consistent with previous results from X-ray and weak lensing observations . This work is the first result from the APEX-SZ experiment , and represents the first reported scientific result from observations with a large array of multiplexed superconducting transition-edge sensor bolometers .