Bullying in schools can be defined as a category of aggressive behaviour with an imbalance of power, and aggression event is repeated over time. Bullying occurs as a social process in nature, and takes place in groups. Attacks are mostly unprovoked, and can be physical or verbal, direct or indirect. This paper focuses on modelling the propagation of bullying in the Spanish school population aged [12, 18] during the period July 2015-January 2020, and on identifying and quantifying its main drivers. Thus, a population dynamics model is built to forecast and quantify the magnitude of the bullying problem in Spain over the July 2015-January 2020 period by taking into account qualitative and quantitative factors; e.g., demography, economy, socio-cultural behaviour, consumption of drugs and alcohol, social contagion and technology. The study provides recommendations to reduce and prevent the growth of this social problem, but to also mitigate a correlated problem, such as intimate partner violence among adults. In fact one of the main utilities of the built model is that new policies can be simulated and allow their effects to be seen.