The precise forecasting of bus arrival times is an important element of implementing on demand city transport. This research uses of Long Short Term Memory (LSTM) networks for predicting bus arrival times in Sofia, Bulgaria. We evaluate the LSTM model against advanced models such as ARIMAX, VARX SARIMAX with Fourier terms Vector Autoregression, Bayesian Fourier models and Backpropagation Neural Networks using Root Mean Squared Error (RMSE) as the performance measure. The results points towards LSTM being better than approaches on routes by adeptly capturing intricate temporal relationships showcasing its promise in dynamic urban transit settings. Moreover the Bayesian Fourier model excels across routes underscoring its ability to accommodate trends effectively. These results suggest that incorporating LSTM networks into on demand transportation systems can notably enhance arrival time forecasts ultimately benefiting passengers and operational efficiency. This study demonstrates the usefulness of machine learning methods in urban transport planning and management by demonstrating how LSTM networks can improve optimization, on demand transportation.