Phage display is a powerful laboratory technique used to study the interactions between proteins and other molecules, whether other proteins, peptides, DNA or RNA. The under-utilisation of this data in conjunction with deep learning models for protein design may be attributed to; high experimental noise levels; the complex nature of data pre-processing; and difficulty interpreting these experimental results. In this work, we propose a novel approach utilising a Bayesian Neural Network within a training loop, in order to simulate the phage display experiment and its associated noise. Our goal is to investigate how understanding the experimental noise and model uncertainty can enable the reliable application of such models to reliably interpret phage display experiments. We validate our approach using actual binding affinity measurements instead of relying solely on proxy values derived from 'held-out' phage display rounds.