We analyze the data of the gravitational microlensing survey carried out by the Microlensing Observations in Astrophysics (MOA) group during 2000 toward the Galactic bulge ( GB). Our observations are designed to detect efficient high-magnification events with faint source stars and short-timescale events, by increasing the sampling rate up to similar to6 times per night and using Difference Image Analysis (DIA). We detect 28 microlensing candidates in 12 GB fields corresponding to 16 deg(2). We use Monte Carlo simulations to estimate our microlensing event detection efficiency, where we construct the I-band extinction map of our GB fields in order to find dereddened magnitudes. We find a systematic bias and large uncertainty in the measured value of the timescale t(E,out) in our simulations. They are associated with blending and unresolved sources, and are allowed for in our measurements. We compute an optical depth tau = 2.59(-064)(+0.84) x 10(-6) toward the GB for events with timescales 0.3 < t(E) < 200 days. We consider disk- disk lensing, and obtain an optical depth tau(bulge) = 3.36(-0.81)(+1/11) x 10(-6)[0.77/(1 - f(disk))] for the bulge component assuming a 23% stellar contribution from disk stars. These observed optical depths are consistent with previous measurements by the MACHO and OGLE groups, and still higher than those predicted by existing Galactic models. We present the timescale distribution of the observed events, and find there are no significant short events of a few days, in spite of our high detection efficiency for short-timescale events down to t(E) similar to 0.3 days. We find that half of all our detected events have high magnification (>10). These events are useful for studies of extrasolar planets.