We use semi-analytic techniques to evaluate the burst sensitivity of designs for the EXIST hard X-ray survey mission. Applying these techniques to the mission design proposed for the Beyond Einstein program, we find that with its very large field-of-view and faint gamma-ray burst detection threshold, EXIST will detect and localize approximately two bursts per day, a large fraction of which may be at high redshift. We estimate that EXIST's maximum sensitivity will be ∼ 4 times greater than that of Swift's Burst Alert Telescope. Bursts will be localized to better than 40 arcsec at threshold, with a burst position as good as a few arcsec for strong bursts. EXIST's combination of three different detector systems will provide spectra from 3 keV to more than 10 MeV. Thus, EXIST will enable a major leap in the understanding of bursts, their evolution, environment, and utility as cosmological probes.Both the HETs and LETs will image the gamma-ray sky using the coded mask technique.