As part of Intelligent Transportation Systems (ITS) public transportation plays a critical and essential role for the mobility in every modern city. In this paper, we introduce a novel method for the real-time prediction of bus arrival times in the various bus stops over a given itinerary. The proposed approach exploits machine and deep learning algorithms, including optimal least square (OLS) linear regression, support vector regression (SVR) and fully-connected neural networks (FNN). The experimental results obtained show that the FNN approach outperforms, in terms of mean absolute prediction error, both SVR (by 7,62 %) and OLS (for 15,74 %).