The trapped Gyro-Landau Fluid (TGLF) model provides fast, accurate predictions of turbulent transport in tokamaks, but whole device simulations requiring thousands of evaluations remain computationally expensive. Neural network (NN) surrogates offer accelerated inference with fully differentiable approximations that enable gradient-based coupling but typically require large training datasets to capture transport flux variations across plasma conditions, creating significant training burden and limiting applicability to expensive gyrokinetic simulations. We propose TGLF-WINN (Wavenumber-Informed NN) with three key innovations: (1) principled feature engineering that reduces target prediction range, simplifying the learning task; (2) physics-guided wavenumber-resolved regularization to improve generalization under sparse data; and (3) Bayesian active learning (BAL) to strategically select training samples based on model uncertainty, reducing data requirements while maintaining accuracy. TGLF-WINN is engineered for data-efficient and robust surrogate training. Feature tuning and wavenumber regularization together deliver a 12.5% relative RMSLE reduction over TGLF-NN when trained on the complete dataset; more importantly, under sparse, unfiltered training conditions (approximately the full dataset size) these two ingredients yield an order-of-magnitude smaller RMSLE degradation than TGLF-NN, a robustness attributable to the wavenumber-informed regularization imposing a physics-guided constraint on per-mode flux contributions. Adding BAL on top, TGLF-WINN matches TGLF-NN’s full-data offline accuracy using only 25% of the training data, reaching RMSLE within 2.8% of TGLF-NN’s full-data baseline and within 4.3% of our own full-data result. We further demonstrate practicality in a downstream flux-matching workflow: the NN surrogate provides a 45 speedup over TGLF while maintaining comparable reconstruction accuracy.