In this paper, we investigate how the drainage and rupture of surfactant-stabilised bubbles floating at the surface of a liquid pool depend on the concentration of surface-active molecules in water. Drainage measurements at the apex of bubbles indicate that the flow profile is increasingly plug-like as the surfactant concentration is decreased from several times the critical micellar concentration (cmc) to just below the cmc. High-speed observations of bubble bursting reveal that the position at which a hole nucleates in the bubble cap also depends on the surfactant concentration. On average, the rupture is initiated close to the bubble foot for low concentrations (<cmc) while its locus moves towards the top of the bubble cap as the concentration increases above the cmc. In order to explain this transition, we propose that marginal regeneration may be responsible for bubble rupture at low concentrations but that bursting at the apex for higher concentrations is driven by gravitational drainage.