Source localization with a geoacoustic model requires optimizing the model over a parameter space of range and depth with the objective of matching a predicted sound field to a field measured on an array. We propose a sample-efficient sequential Bayesian optimization strategy that models the objective function as a Gaussian process (GP) surrogate model conditioned on observed data. Using the mean and covariance functions of the GP, a heuristic acquisition function proposes a candidate in parameter space to sample, balancing exploitation (sampling around the best observed objective function value) and exploration (sampling in regions of high variance in the GP). The candidate sample is evaluated, and the GP conditioned on the updated data. Optimization proceeds sequentially until a fixed budget of evaluations is expended. We demonstrate source localization for a shallow-water waveguide using Monte Carlo simulations and experimental data from an acoustic source tow. Compared to grid search and quasi-random sampling strategies, simulations and experimental results indicate the Bayesian optimization strategy converges on optimal solutions rapidly.