We present CARMA observations in 3.3 mm continuum and several molecular lines of the surroundings of N14, N22, and N74, three infrared bubbles from the GLIMPSE catalog. We have discovered 21 compact continuum sources and confirmed their associations with the bubbles using velocity information from HCO+ and HCN. We have also mapped fragments of quiescent clouds in the vicinity of the bubbles using N₂H+. By combining our data with public survey data, we establish about half of our continuum sources as star-forming cores. We also use survey data with the velocity information from our molecular line observations to describe the morphology of the bubbles and the nature of the fragmentation. We conclude from the properties of the continuum sources that N74 lies at a much greater distance than previously assumed. We also present tentative evidence of molecular clouds being more fragmented on bubble rims compared to dark clouds, suggesting that triggered star formation may occur, though our findings do not conform to a classic collect-and-collapse model.