Cardiac muscle tissue exhibits highly non-linear hyperelastic and orthotropic material behavior during passive deformation. Traditional constitutive identification protocols therefore combine multiple loading modes and typically require multiple specimens and substantial handling. In soft living tissues, such protocols are challenged by inter- and intra-sample variability and manipulation-induced alterations of mechanical response, which can bias inverse calibration. In this work we overcome this gap by exploiting spatially heterogeneous full-field kinematics as an information-rich alternative to multimodal testing. Specifically, we adapt EUCLID, an unsupervised method for the automated discovery of constitutive models, into a Bayesian parameter inference approach for highly non-linear, orthotropic materials and three-dimensional continuum elements. We showcase its strength to qualitatively infer – under varying noise levels – material model parameters of in-silico myocardial tissue slabs from a single heterogeneous biaxial stretch test. Our results show that microstructure-induced and geometry-induced heterogeneity are essential for recovering shear coupling parameters. The inferred responses agree closely with Cauchy stresses from uni-modal deformations using the ground-truth material model parameters and yield credible intervals that reflect the impact of measurement noise on orthotropic material model inference. We also show the generalizing capabilities of the method through high coefficient of correlation R^2 >= 0.9 between inferred and ground-truth strain energy density under mixed-modal deformations. Overall, our work supports single-shot, uncertainty-aware characterization of nonlinear orthotropic material models from a single biaxial test, reducing sample demand and experimental manipulation.