Speech Emotion Recognition (SER) systems have growing applications in sensitive domains such as mental health and education, where biased predictions can cause harm. Traditional fairness metrics, such as Equalised Odds and Demographic Parity, often overlook the joint dependency between demographic attributes and model predictions. We propose a fairness modelling approach for SER that explicitly captures allocative bias by learning the joint relationship between demographic attributes and model error. We validate our fairness metric on synthetic data, then apply it to evaluate HuBERT and WavLM models finetuned on the CREMA-D dataset. Our results indicate that the proposed fairness model captures more mutual information between protected attributes and biases and quantifies the absolute contribution of individual attributes to bias in SSL-based SER models. Additionally, our analysis reveals indications of gender bias in both HuBERT and WavLM.