Most work on musical score models (a.k.a. musical language models) for music transcription has focused on describing the local sequential dependence of notes in musical scores and failed to capture their global repetitive structure, which can be a useful guide for transcribing music. Focusing on rhythm, we formulate several classes of Bayesian Markov models of musical scores that describe repetitions indirectly using the sparse transition probabilities of notes or note patterns. This enables us to construct piece-specific models for unseen scores with an unfixed repetitive structure and to derive tractable inference algorithms. Moreover, to describe approximate repetitions, we explicitly incorporate a process for modifying the repeated notes/note patterns. We apply these models as prior musical score models for rhythm transcription, where piece-specific score models are inferred from performed MIDI data by Bayesian learning, in contrast to the conventional supervised construction of score models. Evaluations using the vocal melodies of popular music showed that the Bayesian models improved the transcription accuracy for most of the tested model types, indicating the universal efficacy of the proposed approach. Moreover, we found an effective data representation for modelling rhythms that maximizes the transcription accuracy and computational efficiency.