The concentration of microbes and other particulates is frequently enriched in the droplets produced by bursting bubbles. As a bubble rises to the ocean surface, particulates in the bulk liquid can be transported to the sea surface microlayer by attaching to the bubble's interface. When the bubble eventually ruptures, a fraction of these particulates is often ejected into the surroundings in film droplets with a particulate concentration that is higher than in the liquid from which they formed. The precise mechanisms responsible for this enrichment are unclear, yet such enrichment at the ocean surface influences important exchange processes with the atmosphere. Here we provide evidence that drainage, coupled with scavenging, is responsible for the enrichment. By simultaneously recording the drainage and rupture effects with high-speed and standard photography, we directly measured the particulate concentrations in the thin film of a bubble cap at the moment before it ruptures. We observed that the enrichment factor strongly depends on the film thickness at rupture, and developed a physical model, based on scavenging and drainage, that is consistent with our observations. We have also demonstrated that this model is quantitatively consistent with prior observations of film drop enrichment, indicating its potential for a broader range of applications in the study of the sea surface microlayer and related phenomena.