Recent research has shown that artificial intelligence (AI) models can exhibit bias in performance when trained using data that are imbalanced by protected attribute(s). Most work to date has focused on deep learning models, but classical AI techniques that make use of hand-crafted features may also be susceptible to such bias. In this paper we investigate the potential for race bias in random forest (RF) models trained using radiomics features. Our application is prediction of tumour molecular subtype from dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) of breast cancer patients. Our results show that radiomics features derived from DCE-MRI data do contain race-identifiable information, and that RF models can be trained to predict White and Black race from these data with 60-70% accuracy, depending on the subset of features used. Furthermore, RF models trained to predict tumour molecular subtype using race-imbalanced data seem to produce biased behaviour, exhibiting better performance on test data from the race on which they were trained.