Equatorial Plasma Bubbles (EPBs) are zones characterized by fluctuations in plasma densities which form in the low-latitude ionosphere primarily during the post-sunset. They subject radio signals to amplitude and phase variabilities, affecting the functioning of technological systems that utilize the Global Navigation Satellite Systems (GNSS) signals for navigation. Thus, understanding EPB occurrence patterns and morphological features is vital for mitigating their effects. In this work, we employed two GNSS receivers and an All-Sky Imager (ASI) to conduct simultaneous observations on the morphology of EPBs over Brazil. The main objectives of the study were (1) to develop a Random Forest (RF) machine-learning model to estimate and predict the zonal drift velocities of EPBs, and (2) to compare the model predictions with actual EPB drifts inferred from the two instruments, as well as zonal neutral wind speeds obtained from the Horizontal Wind Model (HWM-14). In the model development, we utilized reliable EPB drift measurements made during geomagnetically quiet days between 2013 and 2017 in Brazil. The model predicted the velocities based on parameters including the day of the year, universal time, critical frequency of the F2 layer (foF2), solar and interplanetary indices. The correlation coefficients of 0.98 and 0.96 and RMSE values of 10.61 m/s and 10.06 m/s were obtained upon training and validation correspondingly. We evaluated the accuracy of the model in predicting EPB drifts on two geomagnetically quiet nights where an average correlation coefficient of 0.89 and an RMSE of 15.74 m/s were obtained. The predicted drifts, the zonal neutral wind velocities, and the GNSS and ASI velocity measurements were put into context for validation purposes. Overall, the velocities were comparable and ranged between ∼100 m/s and ∼30 m/s from the hours of 00 UT to 05 UT. The results confirmed the accuracy and applicability of the model, revealing the ionosphere-thermosphere coupling influence on the nocturnal propagation of EPBs under the full activation of the F region dynamo.