Bias in generative AI models poses significant challenges as these technologies are increasingly deployed in critical societal domains. This paper presents a comprehensive review of state-of-the-art methods for detecting and mitigating bias in generative AI, with a strong emphasis on fairness, inclusivity, and ethical deployment. We examine advanced techniques such as adversarial testing, statistical bias analysis, and open-set bias detection to reveal the complex and multifaceted nature of bias in AI systems. Furthermore, we detail effective mitigation strategies, including data augmentation, re-sampling, and fairness-aware constraints, alongside post-processing techniques such as equalized odds and calibrated equalized odds. Our findings show that while these techniques improve fairness, they often encounter limitations related to data diversity, algorithmic opacity, and the dynamic nature of bias in real-world settings. We explore these challenges in the context of high-stakes applications like healthcare and law enforcement, where biased AI models can exacerbate social inequalities. To address these limitations, we propose future research directions that emphasize intersectional bias analysis, continuous real-world monitoring, and the need for greater public and regulatory engagement. By advancing detection and mitigation methods, this study contributes to the development of more fair, ethical, and socially responsible generative AI systems. The code supporting our analysis is publicly available on GitHub to ensure transparency and foster collaboration in this critical area of AI research.