The integration of Artificial Intelligence (AI) in public service delivery presents a transformative opportunity for Bangladesh, where bureaucratic inefficiencies, resource limitations, and unequal access to services persist as significant challenges. This study investigates the current applications of AI in society, its socio-economic impact, and challenges within major sectors in Bangladesh. Qualitative approaches, such as Key Informant Interviews with AI experts, as well as literature review was conducted to highlight AI innovations such as telehealth platforms, smart agricultural systems, and AI-enabled educational tools that greatly increase efficiency, accessibility, and equity in public services. Findings demonstrate that AI initiatives affected more than 40 million people by paving ways for flood prediction while enabling 2.7 million students for AI-enabled education and saving up to 87.5% costs in helpline servicing. AI-enabled healthcare provides services to over 600,000 pregnant women, while IoT-based farming systems increase profitability and yield for aquaculture. The future shows bright prospects for AI-related applications in predictive healthcare, urban planning, and sustainable agriculture. Some major challenges are infrastructure deficits, data privacy breaches, lack of digital literacy, and unpreparedness of the workforce. Policy frameworks emphasizing ethical AI use, scaling capacity building, and bridging the digital divide would lead to citizen-centered governance.