The biases exhibited by Text-to-Image (TTI) models are often treated as if they are independent, but in reality, they may be deeply interrelated. Addressing bias along one dimension, such as ethnicity or age, can inadvertently influence another dimension, like gender, either mitigating or exacerbating existing disparities. Understanding these interdependencies is crucial for designing fairer generative models, yet measuring such effects quantitatively remains a challenge. In this paper, we aim to address these questions by introducing BiasConnect, a novel tool designed to analyze and quantify bias interactions in TTI models. Our approach leverages a counterfactual-based framework to generate pairwise causal graphs that reveals the underlying structure of bias interactions for the given text prompt. Additionally, our method provides empirical estimates that indicate how other bias dimensions shift toward or away from an ideal distribution when a given bias is modified. Our estimates have a strong correlation (+0.69) with the interdependency observations post bias mitigation. We demonstrate the utility of BiasConnect for selecting optimal bias mitigation axes, comparing different TTI models on the dependencies they learn, and understanding the amplification of intersectional societal biases in TTI models.