Vision-Language Models (VLMs) have made great strides in everyday visual tasks, such as captioning a natural image, or answering commonsense questions about such images. But humans possess the puzzling ability to deploy their visual reasoning abilities in radically new situations, a skill rigorously tested by the classic set of visual reasoning challenges known as the Bongard problems. We present a neurosymbolic approach to solving these problems: given a hypothesized solution rule for a Bongard problem, we leverage LLMs to generate parameterized programmatic representations for the rule and perform parameter fitting using Bayesian optimization. We evaluate our method on classifying Bongard problem images given the ground truth rule, as well as on solving the problems from scratch.