Using atomic and molecular gas observations from the GASS and COLD GASS surveys and complementary optical/UV data from SDSS and GALEX , we investigate the nature of the variations in the molecular gas depletion time observed across the local massive galaxy population . The large and unbiased COLD GASS sample allows us for the first time to statistically assess the relative importance of galaxy interactions , bar instabilities , morphologies and the presence of AGN in regulating star formation efficiency . We find that both the H _ { 2 } mass fraction and depletion time vary as a function of the distance of a galaxy from the main sequence traced by star-forming galaxies in the SFR- M _ { \ast } plane . The longest gas depletion times are found in below-main sequence bulge-dominated galaxies ( \mu _ { \ast } > 5 \times 10 ^ { 8 } M _ { \odot } kpc ^ { -2 } , C > 2.6 ) that are either gas-poor ( M _ { H _ { 2 } } / M _ { \ast } < 1.5 % ) , or else on average less efficient by a factor of \sim 2 than disk-dominated galaxy at converting into stars any cold gas they may have . We find no link between the presence of AGN and these long depletion times . In the regime where galaxies are disc-dominated and gas-rich , the galaxies undergoing mergers or showing signs of morphological disruptions have the shortest molecular gas depletion times , while those hosting strong stellar bars have only marginally higher global star formation efficiencies as compared to matched control samples . Our interpretation is that the molecular gas depletion time variations are caused by changes in the ratio between the gas mass traced by the CO ( 1-0 ) observations , and the gas mass in high density star-forming cores ( as traced by observations of e.g . HCN ( 1-0 ) ) . While interactions , mergers and bar instabilities can locally increase pressure and raise the ratio of efficiently star-forming gas to CO-detected gas ( therefore lowering the CO-based depletion time ) , massive bulges may prevent the formation of dense clumps by stabilizing gas disks against fragmentation , therefore producing the long depletion times . Building a sample representative of the local galaxy population with M _ { \ast } > 10 ^ { 10 } M _ { \odot } , we derive a global Kennicutt-Schmidt star formation relation of slope 1.18 \pm 0.24 , and observe structure within the scatter around this relation , with galaxies having low ( high ) stellar mass surface densities lying systematically above ( below ) the mean relation , suggesting that \Sigma _ { H _ { 2 } } is not the only parameter driving the global star formation ability of a galaxy .