Consumer-resource interactions are central to ecology, as all organisms rely on consuming resources to survive. Functional responses describe how a consumer's feeding rate changes with resource availability, influenced by processes like searching for, capturing, and handling resources. To study functional responses, experiments typically measure the amount of food consumed—often in discrete units like prey—over a set time. These experiments systematically vary prey availability to observe how it affects the consumer's feeding behaviour. The data generated by such experiments are often analysed using differential equation-based models. Here, we argue that such models do not represent a realistic data-generating process for many such experiments and propose an alternative stochastic individual-based model. This class of models, however, is expensive for inference, and we use machine learning methods to expedite fitting these models to data. We then use our method to do generalised linear model-based inference for a series of experiments conducted on a stickleback fish. Our methodology is made available to others in a Python package for Bayesian hierarchical inference for stochastic, individual-based models of functional responses.