The Milky Way Project citizen science initiative recently increased the number of known infrared bubbles in the inner Galactic plane by an order of magnitude compared to previous studies. We present a detailed statistical analysis of this dataset with the Red MSX Source catalog of massive young stellar sources to investigate the association of these bubbles with massive star formation. We particularly address the question of massive triggered star formation near infrared bubbles. We find a strong positional correlation of massive young stellar objects (MYSOs) and H II regions with Milky Way Project bubbles at separations of < 2 bubble radii. As bubble sizes increase, a statistically significant overdensity of massive young sources emerges in the region of the bubble rims, possibly indicating the occurrence of triggered star formation. Based on numbers of bubble-associated RMS sources we find that 67+/-3% of MYSOs and (ultra)compact H II regions appear associated with a bubble. We estimate that approximately 22+/-2% of massive young stars may have formed as a result of feedback from expanding H II regions. Using MYSO-bubble correlations, we serendipitously recovered the location of the recently discovered massive cluster Mercer 81, suggesting the potential of such analyses for discovery of heavily extincted distant clusters.