Precise control of filament formation remains a central barrier in extrusion-based bioprinting, where small deviations in material behavior can lead to large variations in structure and cellular outcome. Here, we present a data-driven rheology framework that enables predictive embedded bioprinting by directly linking material behavior to process outcome. A machine learning (ML) model was used to capture the coupled temperature-shear response of a thermosensitive GelMA bioink and the shear-dependent behavior of the supporting bath, and was integrated into process analysis. This approach improved the prediction of both flow disturbance and filament geometry, with reduced errors in aspect ratio and filament width compared to conventional constitutive models. The improved predictability translated into controllable fabrication, enabling stable filament formation across a wide size range (≈160-800 μm) and the reliable construction of ultra-soft, freeform, and overhanging structures with preserved three-dimensional fidelity. This level of control also carried biological consequences, as well-defined filaments supported faster post-printing recovery, enhanced alignment, stronger MHC expression, and transcriptional signatures consistent with a more favorable differentiation state. These results show that improving rheological description could move embedded bioprinting toward predictive manufacturing, where geometry and biological outcome can be coordinated through material-informed design.