Artificial Intelligence (AI) software systems, such as Sentiment Analysis (SA) systems, typically learn from large amounts of data that may reflect human biases. Consequently, the machine learning model in such software systems may exhibit unintended demographic bias based on specific characteristics (e.g., gender, occupation, country-of-origin, etc.). Such biases manifest in an SA system when it predicts a different sentiment for similar texts that differ only in the characteristic of individuals described. Existing studies on revealing bias in SA systems rely on the production of sentences from a small set of short, predefined templates. To address this limitation, we present BisaFinder, an approach to discover biased predictions in SA systems via metamorphic testing. A key feature of BisaFinder is the automatic curation of suitable templates based on the pieces of text from a large corpus, using various Natural Language Processing (NLP) techniques to identify words that describe demographic characteristics. Next, BisaFinder instantiates new text from these templates by filling in placeholders with words associated with a class of a characteristic (e.g., gender-specific words such as female names, "she", "her"). These texts are used to tease out bias in an SA system. BisaFinder identifies a bias-uncovering test case when it detects that the SA system exhibits demographic bias for a pair of texts, i.e., it predicts a different sentiment for texts that differ only in words associated with a different class (e.g., male vs. female) of a target characteristic (e.g., gender). Our empirical evaluation showed that BisaFinder can effectively create a large number of realistic and diverse test cases that uncover various biases in an SA system with a high true positive rate of up to 95.8\%.