From the intimate realm of personal interactions to the sprawling arena of political discourse, discerning the trustworthy from the dubious is crucial. Here, we present a novel behavioral task and accompanying Bayesian models that allow us to study key aspects of this learning process in a tightly controlled setting. In our task, participants are confronted with several different types of (mis-)information sources, ranging from ones that lie to ones with biased reporting, and have to learn these attributes under varying degrees of feedback. We formalize inference in this setting as a doubly Bayesian learning process where agents simultaneously learn about the ground truth as well as the qualities of an information source reporting on this ground truth. Our model and detailed analyses reveal how participants can generally follow Bayesian learning dynamics, highlighting a basic human ability to learn about diverse information sources. This learning is also reflected in explicit trust reports about the sources. We additionally show how participants approached the inference problem with priors that held sources to be helpful. Finally, when outside feedback was noisier, participants still learned along Bayesian lines but struggled to pick up on biases in information. Our work pins down computationally the generally impressive human ability to learn the trustworthiness of information sources while revealing minor fault lines when it comes to noisier environments and news sources with a slant.