There exists strong experimental evidence that bainitic ferrite is formed as a supersaturated solid solution of carbon within a tetragonally-distorted body-centered iron structure (BCT), where carbon preferentially occupies the octahedral site. Despite this, the BCT structure has not yet been accounted for in the computational analysis of the thermodynamics of the bainite transformation. In the present work, we propose to calculate the onset of the bainite transformation based on the T₀′ concept, including the effect of Zener-ordering. This mechanism stabilizes the BCT structure, makes it energetically more favorable than BCC and leads to a significantly higher solubility of C compared Fe-BCC. The computational predictions are made based on a recent reassessment of low-T Gibbs energies and finally compared to experiments. The important role of C is emphasized, with the Fe-C system used as a showcase.