The auditory brainstem response (ABR) can be used to evaluate hearing sensitivity of animals. However, typical measurement protocols are time-consuming. Here, an adaptive algorithm is proposed for efficient ABR threshold estimation. The algorithm relies on the update of the predicted hearing threshold from a Gaussian process model as ABR data are collected using iteratively optimized stimuli. To validate the algorithm, ABR threshold estimation is simulated by adaptively subsampling pre-collected ABR datasets. The simulated experiment is performed on 5 datasets of mouse, budgerigar, gerbil, and guinea pig ABRs (27 ears). The datasets contain 68-106 stimuli conditions, and the adaptive algorithm is configured to terminate after 20 stimuli conditions. The algorithm threshold estimate is compared against human rater estimates who visually inspected the full waveform stacks. The algorithm threshold matches the human estimates within 10 dB, averaged over frequency, for 15 of the 27 ears while reducing the number of stimuli conditions by a factor of 3-5 compared to standard practice. The intraclass correlation coefficient is 0.81 with 95% upper and lower bounds at 0.74 and 0.86, indicating moderate to good reliability between human and algorithm threshold estimates. The results demonstrate the feasibility of a Bayesian adaptive procedure for rapid ABR threshold estimation.