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While it is clear that Type Ia supernovae (SNe) are the result of thermonuclear explosions in C/O white dwarfs (WDs), a great deal remains uncertain about the binary companion that facilitates the explosive disruption of the WD. Here, we present a comprehensive analysis of a large, unique data set of 127 SNe Ia with exquisite coverage by the Zwicky Transient Facility (ZTF). High-cadence (six observations per night) ZTF observations allow us to measure the SN rise time and examine its initial evolution. We develop a Bayesian framework to model the early rise as a power law in time, which enables the inclusion of priors in our model. For a volume-limited subset of normal SNe Ia, we find that the mean power-law index is consistent with 2 in the r(ZTF)-band (alpha(r) = 2.01 +/- 0.02), as expected in the expanding fireball model. There are, however, individual SNe that are clearly inconsistent with alpha(r) = 2. We estimate a mean rise time of 18.9 days (with a range extending from similar to 15 to 22 days), though this is subject to the adopted prior. We identify an important, previously unknown, bias whereby the rise times for higherredshift SNe within a flux-limited survey are systematically underestimated. This effect can be partially alleviated if the power-law index is fixed to alpha = 2, in which case we estimate a mean rise time of 21.7 days (with a range from similar to 18 to 23 days). The sample includes a handful of rare and peculiar SNe Ia. Finally, we conclude with a discussion of lessons learned from the ZTF sample that can eventually be applied to observations from the Vera C..Rubin Observatory., QC 20220922Nordita SU