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Artificial intelligence (AI) methods are being used increasingly for the automated segmentation of cine cardiac magnetic resonance (CMR) imaging. However, these methods have been shown to be subject to race bias, i.e. they exhibit different levels of performance for different races depending on the (im)balance of the data used to train the AI model. In this paper we investigate the source of this bias, seeking to understand its root cause(s) so that it can be effectively mitigated. We perform a series of classification and segmentation experiments on short-axis cine CMR images acquired from Black and White subjects from the UK Biobank and apply AI interpretability methods to understand the results. In the classification experiments, we found that race can be predicted with high accuracy from the images alone, but less accurately from ground truth segmentations, suggesting that the distributional shift between races, which is often the cause of AI bias, is mostly image-based rather than segmentation-based. The interpretability methods showed that most attention in the classification models was focused on non-heart regions, such as subcutaneous fat. Cropping the images tightly around the heart reduced classification accuracy to around chance level. Similarly, race can be predicted from the latent representations of a biased segmentation model, suggesting that race information is encoded in the model. Cropping images tightly around the heart reduced but did not eliminate segmentation bias. We also investigate the influence of possible confounders on the bias observed.