We present Colibri, an open-source Python framework for parton distribution function (PDF) determination, designed to provide a flexible and efficient environment for both frequentist and Bayesian inference. Colibri allows users to implement custom PDF models while leveraging built-in tools for fast observable computation, access to experimental data, and uncertainty propagation via Hessian, Monte Carlo replica, and numerical Bayesian sampling methods. As a first realistic application, we introduce a Bayesian PDF determination based on linear models, where PDFs are represented in a low-dimensional functional basis obtained from the dimensional reduction of a neural-network space. This compact representation enables fast inference, transparent control of model complexity, and principled Bayesian model selection. The methodology is validated through closure tests on Deep Inelastic Scattering data, illustrating Colibri's capability to benchmark different uncertainty estimation strategies and paving the way for scalable Bayesian PDF fits relevant for LHC phenomenology.