Citizen science has helped astronomers comb through large data sets to identify patterns and objects that are not easily found through automated processes. The Milky Way Project (MWP), a citizen science initiative on the Zooniverse platform, presents internet users with infrared (IR) images from Spitzer Space Telescope Galactic plane surveys. MWP volunteers make classification drawings on the images to identify targeted classes of astronomical objects. We present the MWP second data release (DR2) and an updated data reduction pipeline written in Python. We aggregate 3 million classifications made by MWP volunteers during the years 2012-2017 to produce the DR2 catalogue, which contains 2600 IR bubbles and 599 candidate bow-shock driving stars. The reliability of bubble identifications, as assessed by comparison to visual identifications by trained experts and scoring by a machine-learning algorithm, is found to be a significant improvement over DR1. We assess the reliability of IR bow shocks via comparison to expert identifications and the colours of candidate bow-shock driving stars in the 2MASS point-source catalogue. We hence identify highly-reliable subsets of 1394 DR2 bubbles and 453 bow-shock driving stars. Uncertainties on object coordinates and bubble size/shape parameters are included in the DR2 catalog. Compared with DR1, the DR2 bubbles catalogue provides more accurate shapes and sizes. The DR2 catalogue identifies 311 new bow shock driving star candidates, including three associated with the giant HII regions NGC 3603 and RCW 49.