Microscopic organisms, such as bacteria, have the ability of colonizing surfaces and developing biofilms that can determine diseases and infections. Most bacteria secrete a significant amount of extracellular polymer substances that are relevant for biofilm stabilization and growth. In this work, we apply computer simulation and perform experiments to investigate the impact of polymer size and concentration on early biofilm formation and growth. We observe as bacterial cells formed loose, disorganized clusters whenever the effect of diffusion exceeded that of cell growth and division. Addition of model polymeric molecules induced particle self-assembly and aggregation to form compact clusters in a polymer size- and concentration-dependent fashion. We also find that large polymer size or concentration lead to the development of intriguing stripe-like and dendritic colonies. The results obtained by Brownian dynamic simulation closely resemble the morphologies that we experimentally observe in biofilms of a Pseudomonas Putida strain with added polymers. The analysis of the Brownian dynamic simulation results suggests the existence of a threshold polymer concentration that distinguishes between two growth regimes. Below this threshold, the main force driving polymer-induced compaction is hindrance of bacterial cell diffusion, while collective effects play a minor role. Above this threshold, especially for large polymers, polymer-induced compaction is a collective phenomenon driven by depletion forces. Well above this concentration threshold, severely limited diffusion drives the formation of filaments and dendritic colonies.