Bus transit plays a vital role in urban public transportation but often struggles to provide accurate and reliable departure times. This leads to delays, passenger dissatisfaction, and decreased ridership, particularly in transit-dependent areas. A major challenge lies in the discrepancy between actual and scheduled bus departure times, which disrupts timetables and impacts overall operational efficiency. To address these challenges, this paper presents a neural network-based approach for real-time bus departure time prediction tailored for smart IoT public transit applications. We leverage AI-driven models to enhance the accuracy of bus schedules by preprocessing data, engineering relevant features, and implementing a fully connected neural network that utilizes historical departure data to predict departure times at subsequent stops. In our case study analyzing bus data from Boston, we observed an average deviation of nearly 4 minutes from scheduled times. However, our model, evaluated across 151 bus routes, demonstrates a significant improvement, predicting departure time deviations with an accuracy of under 80 seconds. This advancement not only improves the reliability of bus transit schedules but also plays a crucial role in enabling smart bus systems and IoT applications within public transit networks. By providing more accurate real-time predictions, our approach can facilitate the integration of IoT devices, such as smart bus stops and passenger information systems, that rely on precise data for optimal performance.