This paper presents geoacoustic inversion of a light bulb implosion recorded during the Shallow Water 2006 experiment. The source is low frequency and impulsive, the environment is shallow water, and the acoustic signal is recorded using a single receiver. In this context, propagation is described by modal theory, and inversion is carried out by matching modal dispersion curves in the time-frequency domain. Experimental dispersion curves are estimated using an advanced signal processing method called warping, allowing inversion to be carried out at a relatively short range (~/=7 km). Moreover, the inversion itself is performed using Bayesian methodology. This allows inference of the seabed structure from the data, including the number of seabed layers resolved, optimal estimates of the seabed parameters, and quantitative uncertainty estimates. Inversion results of the experimental data are in good agreement with both ground truth and estimates from other experimental data in the same region.