Over-the-air (OTA) federated learning (FL) has been well recognized as a scalable paradigm that exploits the waveform superposition of the wireless multiple-access channel to aggregate model updates simultaneously. Existing OTA-FL designs largely enforce zero-bias model updates by either assuming homogeneous wireless conditions (equal path loss across devices) or forcing zero bias updates to guarantee convergence. Under heterogeneous wireless scenarios, however, such unbiased designs are constrained by the worst-channel device and suffer from high variance in the updates. Moreover, prior analyses of biased OTAFL largely focus on convex objectives, whereas most modern machine-learning models are highly non-convex. Motivated by these gaps, we study OTA-FL with stochastic gradient descent (SGD) for smooth non-convex objectives under wireless heterogeneity. We develop novel OTA-FL SGD updates that allow a structured, time-invariant model bias while facilitating reduced variance in the updates. We also derive a finite-time stationarity bound (expected time average squared gradient norm) that explicitly reveals a bias–variance trade-off. To optimize this trade-off, we pose a non-convex joint OTA power-control design and develop an efficient successive convex approximation (SCA) algorithm that requires only statistical CSI of the devices at the base station. Experiments on a non-convex image classification task validate the approach: the SCA-based design accelerates convergence via an optimized bias and improves generalization over prior OTA-FL baselines.