We propose a semester-long Bayesian statistics course for undergraduate students with calculus and probability background. We cultivate students' Bayesian thinking with Bayesian methods applied to real data problems. We leverage modern Bayesian computing techniques not only for implementing Bayesian methods, but also to deepen students' understanding of the methods. Collaborative case studies further enrich students' learning and provide experience to solve open-ended applied problems. The course has an emphasis on undergraduate research, where accessible academic journal articles are read, discussed, and critiqued in class. With increased confidence and familiarity, students take the challenge of reading, implementing, and sometimes extending methods in journal articles for their course projects. Supplementary materials for this article are available online.