Large language models (LLMs) are known to perpetuate stereotypes and exhibit biases. Various strategies have been proposed to mitigate these biases, but most work studies biases as a black-box problem without considering how concepts are represented within the model. We adapt techniques from representation engineering to study how the concept of "gender" is represented within LLMs. We introduce a new method that extracts concept representations via probability weighting without labeled data and efficiently selects a steering vector for measuring and manipulating the model's representation. We develop a projection-based method that enables precise steering of model predictions and demonstrate its effectiveness in mitigating gender bias in LLMs and show that it also generalizes to racial bias. Our code is available at: https://github.com/hannahxchen/gender-bias-steering