Still recently, bacterial fluid suspensions have motivated a lot of works, both experimental and theoretical, with the objective to understand their collective dynamics from universal and simple rules. Since some species are active, most of these works concern the strong interactions that these bacteria exert on a forced flow leading to instabilities, chaos and turbulence. Here, we investigate the self-organization of expanding bacterial colonies under chemotaxis, proliferation and eventually active-reaction. We propose a simple model to understand and quantify the physical properties of these living organisms which either give cohesion or on the contrary dispersion to the colony. Taking into account the diffusion and capture of morphogens complicates the model since it induces a bacterial density gradient coupled to bacterial density fluctuations and dynamics. Nevertheless under some specific conditions, it is possible to investigate the pattern formation as a usual viscous fingering instability. This explains the similarity and differences of patterns according to the physical bacterial suspension properties and explain the factors which favor compactness or branching.