Understanding biases and stereotypes encoded in the weights of Large Language Models (LLMs) is crucial for developing effective mitigation strategies. However, biased behaviour is often subtle and non-trivial to isolate, even when deliberately elicited, making systematic analysis and debiasing particularly challenging. To address this, we introduce \texttt{BiasGym}, a simple, cost-effective, and generalizable framework for reliably and safely injecting, analyzing, and mitigating conceptual associations of biases within LLMs. \texttt{BiasGym} consists of two components: \texttt{BiasInject}, which safely injects specific biases into the model via token-based fine-tuning while keeping the model frozen, and \texttt{BiasScope}, which leverages these injected signals to identify and reliably steer the components responsible for biased behavior. Our method enables consistent bias elicitation for mechanistic analysis, supports targeted debiasing without degrading performance on downstream tasks, and generalizes to biases unseen during fine-tuning. We demonstrate the effectiveness of BiasGym in reducing real-world stereotypes (e.g., people from Italy being `reckless drivers'), showing its utility for both safety interventions and interpretability research.