We have previously found [J. Eggers, M. A. Fontelos, D. Leppinen, and J. H. Snoeijer, Phys. Rev. Lett., 98 (2007), 094502] that the pinch-off of a gas bubble in an inviscid environment is controlled by scaling exponents which are slowly varying in time. To leading order, these results did not require the spatial profile of the interface near break-up. Here we refine our previous analysis by computing the entire shape of the neck. The neck shape is characterized by similarity functions that are also slowly varying on a logarithmic scale. We compare these results to experiments and find agreement within the experimentally accessible range. More detailed confirmation of the asymptotic analysis is provided by the excellent agreement with numerical simulations of the bubble pinch-off.