The first JWST observations of nearby galaxies have unveiled a rich population of bubbles that trace the stellar-feedback mechanisms responsible for their creation. Studying these bubbles therefore allows us to chart the interaction between stellar feedback and the interstellar medium, and the larger galactic flows needed to regulate star formation processes globally. We present the first catalog of bubbles in NGC 628, visually identified using Mid-Infrared Instrument F770W Physics at High Angular resolution in Nearby GalaxieS (PHANGS)-JWST observations, and use them to statistically evaluate bubble characteristics. We classify 1694 structures as bubbles with radii between 6 and 552 pc. Of these, 31% contain at least one smaller bubble at their edge, indicating that previous generations of star formation have a local impact on where new stars form. On large scales, most bubbles lie near a spiral arm, and their radii increase downstream compared to upstream. Furthermore, bubbles are elongated in a similar direction to the spiral-arm ridgeline. These azimuthal trends demonstrate that star formation is intimately connected to the spiral-arm passage. Finally, the bubble size distribution follows a power law of index p = -2.2 +/- 0.1, which is slightly shallower than the theoretical value by 1-3.5 sigma that did not include bubble mergers. The fraction of bubbles identified within the shells of larger bubbles suggests that bubble merging is a common process. Our analysis therefore allows us to quantify the number of star-forming regions that are influenced by an earlier generation, and the role feedback processes have in setting the global star formation rate. With the full PHANGS-JWST sample, we can do this for more galaxies.