Measuring the auditory lateralization elicited by interaural time difference (ITD) cues involves the estimation of a psychometric function (PF). The shape of this function usually follows from the analysis of the subjective data and models the probability of correctly localizing the angular position of a sound source. The present study describes and evaluates a procedure for progressively fitting a PF, using Gaussian process classification of the subjective responses produced during a binary decision experiment. The process refines adaptively an approximated PF, following Bayesian inference. At each trial, it suggests the most informative auditory stimulus for function refinement according to Bayesian active learning by disagreement (BALD) mutual information. In this paper, the procedure was modified to accommodate two-alternative forced choice (2AFC) experimental methods and then was compared with a standard adaptive “three-down, one-up” staircase procedure. Our process approximates the average threshold ITD 79.4% correct level of lateralization with a mean accuracy increase of 8.9% over the Weibull function fitted on the data of the same test. The final accuracy for the Just Noticeable Difference (JND) in ITD is achieved with only 37.6% of the trials needed by a standard lateralization test.