We present an analysis of a densely repeating sample of bursts from the first repeating fast radio burst, FRB 121102. We reanalyzed the data used by Gourdji+ (2019ApJ...877L..19G) and detected 93 additional bursts using our single-pulse search pipeline. In total, we detected 133 bursts in three hours of data at a center frequency of 1.4GHz using the Arecibo telescope, and develop robust modeling strategies to constrain the spectro-temporal properties of all of the bursts in the sample. Most of the burst profiles show a scattering tail, and burst spectra are well modeled by a Gaussian with a median width of 230MHz. We find a lack of emission below 1300MHz, consistent with previous studies of FRB 121102. We also find that the peak of the log-normal distribution of wait times decreases from 207 to 75s using our larger sample of bursts, as compared to that of Gourdji et al. Our observations do not favor either Poissonian or Weibull distributions for the burst rate distribution. We searched for periodicity in the bursts using multiple techniques, but did not detect any significant period. The cumulative burst energy distribution exhibits a broken power-law shape, with the lower- and higher-energy slopes of -0.4+/-0.1 and -1.8+/-0.2, with the break at (2.3+/-0.2)x10^37^erg.