Bainite is a steel microstructure with useful properties for the industry. It combines a high toughness with a hardness value between that of pearlitic and martensitic steels. It occurs as upper and lower bainite which can be distinguished by the size and place of carbides precipitating from austenite or bainitic ferrite, respectively. While the phase transformation from austenite to bainitic ferrite is considered to be displacive, the subsequent carbon diffusion is crucial to the precipitation of carbides and in turn crucial to the formation of the two different morphologies, upper and lower bainite. In this work a phase field model is presented describing the complex transformation from austenite to upper and lower bainite, considering the displacive phase transition from austenite to bainitic ferrite, different diffusion mechanisms, the precipitation of carbides and anisotropic growth due to eigenstrains. The model uses a thermodynamic framework which is derived in this work. The framework is based on generalized stresses and forces providing a strict distinction between universal laws, such as the first and second law of thermodynamics, and constitutive equations which are chosen for the actual transformation process. Prototype models are proposed and numerically solved using the finite element method. The results show the capability of the derived thermodynamic framework and the expected behaviour of bainite.