Protein polymerization and bundling play a central role in cell physiology. Predictive modeling of these processes remains an open challenge, especially when the proteins involved become large and their concentrations high. We present an effective kinetics model of filament formation, bundling and depolymerization following GTP-hydrolysis, which involves a relatively small number of species and reactions, and remains robust over a wide range of concentrations and time scales. We apply this general model to study assembly of FtsZ protein, a basic element in the division process of prokaryotic cells such as Escherichia coli, Bacillus subtilis or Caulobacter crescentus. This analysis demonstrates that our model outperforms its counterparts in terms of both accuracy and computational efficiency. Since our model comprises "only" seventeen ordinary differential equations (ODEs), its computational cost is orders of magnitude smaller than the current alternatives consisting of up to a thousand ODEs. It also provides a new insight into the characteristics and functioning of FtsZ proteins at high concentrations. The simplicity and versatility of our model render it a powerful computational tool, which can be used either as a stand alone descriptor of other biopolymers' assembly or as a component in more complete kinetic models.