The cosmic microwave background (CMB) radiation holds a wealth of information about the evolution of the universe. In particular, measurement of the B-mode polarization pattern of the CMB is a direct probe of the physics of inflation. The E and B Experiment (EBEX) was a balloon-borne telescope designed to search for inflation's signature on the polarization of the CMB. To achieve the high receiver sensitivity necessary to measure a small polarization signal, I assembled, tested, and integrated a kilopixel array of transition edge sensor bolometers. I worked with the fabrication team at UC Berkeley to modify and optimize the bolometer design for the space-like environment at a float altitude of 36 km. The detector characterization measurements, I performed in test cryostats and in EBEX itself, are reported here. I measured the bolometer normal resistances, thermal conductances, critical temperatures, optical efficiencies, time constants, and noise equivalent powers. I also report on the detector performance, with a particular focus on sensitivity and noise, from the 2013 Antarctic flight.