Relationships between genetic alterations, such as co-occurrence or mutual exclusivity, are often observed in cancer, where their understanding may provide new insights into etiology and clinical management. In this study, we combined statistical analyses and computational modelling to explain patterns of genetic alterations seen in 178 patients with bladder tumours (either muscle-invasive or non-muscle-invasive). A statistical analysis on frequently altered genes identified pair associations including co-occurrence or mutual exclusivity. Focusing on genetic alterations of protein-coding genes involved in growth factor receptor signalling, cell cycle and apoptosis entry, we complemented this analysis with a literature search to focus on nine pairs of genetic alterations of our dataset, with subsequent verification in three other datasets available publically. To understand the reasons and contexts of these patterns of associations while accounting for the dynamics of associated signalling pathways, we built a logical model. This model was validated first on published mutant mice data, then used to study patterns and to draw conclusions on counter-intuitive observations, allowing one to formulate predictions about conditions where combining genetic alterations benefits tumorigenesis. For example, while CDKN2A homozygous deletions occur in a context of FGFR3 activating mutations, our model suggests that additional PIK3CA mutation or p21CIP deletion would greatly favour invasiveness. Further, the model sheds light on the temporal orders of gene alterations, for example, showing how mutual exclusivity of FGFR3 and TP53 mutations is interpretable if FGFR3 is mutated first. Overall, our work shows how to predict combinations of the major gene alterations leading to invasiveness.