This letter applies trans-dimensional Bayesian geoacoustic inversion to quantify the uncertainty due to model selection when inverting bottom-loss data derived from wind-driven ambient-noise measurements. A partition model is used to represent the seabed, in which the number of layers, their thicknesses, and acoustic parameters are unknowns to be determined from the data. Exploration of the parameter space is implemented using the Metropolis-Hastings algorithm with parallel tempering, whereas jumps between parameterizations are controlled by a reversible-jump Markov chain Monte Carlo algorithm. Sediment uncertainty profiles from inversion of simulated and experimental data are presented.