We present an analysis of a densely repeating sample of bursts from the first repeating fast radio burst, FRB 121102. We detected a total of 133 bursts in 3 hours of data at a center frequency of 1.4 GHz using the Arecibo Telescope, and develop robust modeling strategies to constrain the spectro-temporal properties of all 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 230 MHz. We find a lack of emission below 1300 MHz, consistent with previous studies of FRB 121102. We also find that the peak of the log-normal distribution of wait times decreases from 207 s to 75 s using our larger sample of bursts. 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 $-0.4pm0.1$ and $-1.8pm0.2$, with the break at $(2.3pm0.2)times 10^{37}$ ergs. We provide our burst fitting routines as a python package textsc{burstfit}. All the other analysis scripts and results are publicly available.
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