Passive acoustic monitoring (PAM) studies generate thousands of hours of audio, which may be used to monitor specific animal populations, conduct broad biodiversity surveys, detect threats such as poachers, and more. Machine learning classifiers for species identification are increasingly being used to process the vast amount of audio generated by bioacoustic surveys, expediting analysis and increasing the utility of PAM as a management tool. In common practice, a threshold is applied to classifier output scores, and scores above the threshold are aggregated into a detection count. The choice of threshold produces biased counts of vocalizations, which are subject to false positive/negative rates that may vary across subsets of the dataset. In this work, we advocate for directly estimating call density: The proportion of detection windows containing the target vocalization, regardless of classifier score. Our approach targets a desirable ecological estimator and provides a more rigorous grounding for identifying the core problems caused by distribution shifts -- when the defining characteristics of the data distribution change -- and designing strategies to mitigate them. We propose a validation scheme for estimating call density in a body of data and obtain, through Bayesian reasoning, probability distributions of confidence scores for both the positive and negative classes. We use these distributions to predict site-level densities, which may be subject to distribution shifts. We test our proposed methods on a real-world study of Hawaiian birds and provide simulation results leveraging existing fully annotated datasets, demonstrating robustness to variations in call density and classifier model quality.