Federated Learning (FL) has emerged as a transformative approach in healthcare, enabling collaborative model training across decentralized data sources while preserving user privacy. However, performance of FL rapidly degrades in practical scenarios due to the inherent bias in non Independent and Identically distributed (non-IID) data among participating clients, which poses significant challenges to model accuracy and generalization. Therefore, we propose the Bias-Aware Client Selection Algorithm (BACSA), which detects user bias and strategically selects clients based on their bias profiles. In addition, the proposed algorithm considers privacy preservation, fairness and constraints of wireless network environments, making it suitable for sensitive healthcare applications where Quality of Service (QoS), privacy and security are paramount. Our approach begins with a novel method for detecting user bias by analyzing model parameters and correlating them with the distribution of class-specific data samples. We then formulate a mixed-integer non-linear client selection problem leveraging the detected bias, alongside wireless network constraints, to optimize FL performance. We demonstrate that BACSA improves convergence and accuracy, compared to existing benchmarks, through evaluations on various data distributions, including Dirichlet and class-constrained scenarios. Additionally, we explore the trade-offs between accuracy, fairness, and network constraints, indicating the adaptability and robustness of BACSA to address diverse healthcare applications.