The front of a compact bacterial colony growing on a Petri dish is a paradigmatic instance of non-equilibrium fluctuations in the celebrated Eden, or Kardar-Parisi-Zhang (KPZ), universality class. While in many experiments the scaling exponents crucially differ from the expected KPZ values, the source of this disagreement has remained poorly understood. We have performed growth experiments with B. subtilis 168 and E. coli ATCC 25922 under conditions leading to compact colonies in the classically alleged Eden regime, where individual motility is suppressed. Non-KPZ scaling is indeed observed for all accessible times, KPZ asymptotics being ruled out for our experiments due to the monotonic increase of front branching with time. Simulations of an effective model suggest the occurrence of transient nonuniversal scaling due to diffusive morphological instabilities, agreeing with expectations from detailed models of the relevant biological reaction-diffusion processes.