We examine the problem of planning dives for an Autonomous Underwater Vehicle (AUV) to generate a dense bathymetric map using sidescan sonar. The three key challenges in this scenario are (1) proper modeling of the local uncertainty of the 3D reconstruction, (2) efficient dive planning to reduce this uncertainty, and (3) determination of when to re-plan adaptively based on new information. To address these challenges, we propose using non-parametric Bayesian regression to model the expected accuracy of the map, which provides principled cost functions for planning subsequent dives. In addition, we propose an efficient greedy method to reduce this uncertainty, and we show that it achieves theoretically bounded performance given assumptions on the sensor model and the form of the uncertainty function. We present experiments on the propeller-driven YSI EcoMapper AUV equipped with a sidescan sonar in an inland lake. The experiments demonstrate the benefit of efficient dive planning, with our results providing performance gains of up to 83% versus standard lawnmower patterns.