Bay spent 5 seasons in the Mets organization. He spent the 2011 season with the GCL Mets, before going to Kingsport in 2012. The 2013 season brought Shane to Brooklyn, where an injury limited him to just 3 games, going 0-0 with an ERA of 1.80 in 5 innings pitched.
Bay had an All Star Season in 2014, as he appeared as a reliever in 20 games. He converted 15 of 15 possible saves, which tied the league high. In 22.2 innings pitched, Bay gave up just 4 earned runs, none of which affected the outcome of a game, giving him an ERA of 1.59. In the 2014 All Star Game, Bay pitched a shutout 9th inning.
Bay spent the 2015 season in Savannah where he pitched in 9 games early in the season. In 9 innings pitched, Bay gave up 6 earned runs, resulting in an ERA of 6.00.
For his Mets career, Bay went 1-4 with an ERA of 2.77 in 61.2 innings pitched over 48 games. He converted 21 of 23 save opportunities.