Across a range of biological processes, cells undergo coordinated changes in gene expression, resulting in transcriptome dynamics that unfold within a low-dimensional manifold. Single-cell RNA-sequencing (scRNA-seq) only measures temporal snapshots of gene expression. However, information on the underlying low-dimensional dynamics can be extracted using RNA velocity, which models unspliced and spliced RNA abundances to estimate the rate of change of gene expression. Available RNA velocity algorithms can be fragile and rely on heuristics that lack statistical control. Moreover, the estimated vector field is not dynamically consistent with the traversed gene expression manifold. Here, we develop a generative model of RNA velocity and a Bayesian inference approach that solves these problems. Our model couples velocity field and manifold estimation in a reformulated, unified framework, so as to coherently identify the parameters of an autonomous dynamical system. Focusing on the cell cycle, we implemented VeloCycle to study gene regulation dynamics on one-dimensional periodic manifolds and validated using live-imaging its ability to infer actual cell cycle periods. We benchmarked RNA velocity inference with sensitivity analyses and demonstrated one- and multiple-sample testing. We also conducted Markov chain Monte Carlo inference on the model, uncovering key relationships between gene-specific kinetics and our gene-independent velocity estimate. Finally, we applied VeloCycle to in vivo samples and in vitro genome-wide Perturb-seq, revealing regionally-defined proliferation modes in neural progenitors and the effect of gene knockdowns on cell cycle speed. Ultimately, VeloCycle expands the scRNA-seq analysis toolkit with a modular and statistically rigorous RNA velocity inference framework.