Diffusion and flow matching models have recently emerged as promising approaches for peptide binder design. Despite their progress, these models still face two major challenges. First, categorical sampling of discrete residue types collapses their continuous parameters into one-hot assignments, while continuous variables (e.g., atom positions) evolve smoothly throughout the generation process. This mismatch disrupts the update dynamics and results in suboptimal performance. Second, current models assume unimodal distributions for side-chain torsion angles, which conflicts with the inherently multimodal nature of side-chain rotameric states and limits prediction accuracy. To address these limitations, we introduce PepBFN, the first Bayesian flow network for full-atom peptide design that directly models parameter distributions in fully continuous space. Specifically, PepBFN models discrete residue types by learning their continuous parameter distributions, enabling joint and smooth Bayesian updates with other continuous structural parameters. It further employs a novel Gaussian mixture–based Bayesian flow to capture the multimodal side-chain rotameric states and a Matrix Fisher–based Riemannian flow to directly model residue orientations on the $\mathrm{SO(3)}$ manifold. Together, these parameter distributions are progressively refined via Bayesian updates, yielding smooth and coherent peptide generation. Experiments on side-chain packing, reverse folding, and binder design tasks demonstrate the strong potential of PepBFN in computational peptide design.