A two-dimensional bubble at rest near the surface of a semi-infinite liquid layer is considered. A lubrication analysis of the thin film above the bubble is matched to a capillary-static solution for the outer geometry. Analysis of a transition region between the thinning viscous film and the capillary-static solution leads to an effective boundary condition to be applied at the edge of the film. The result is a description of the drainage of liquid out of the film under gravity and surface tension. This drainage is ultimately responsible for rupture of the film and hence bursting of the bubble.