Training a machine learning model with federated edge learning (FEEL) is typically time-consuming due to the constrained computation power of edge devices and limited wireless resources in edge networks. In this paper, the training time minimization problem is investigated in a quantized FEEL system, where the heterogeneous edge devices send quantized gradients to the edge server via orthogonal channels. In particular, a stochastic quantization scheme is adopted for compression of uploaded gradients, which can reduce the burden of per-round communication but may come at the cost of increasing number of communication rounds. The training time is modeled by taking into account the communication time, computation time and the number of communication rounds. Based on the proposed training time model, the intrinsic trade-off between the number of communication rounds and per-round latency is characterized. Specifically, we analyze the convergence behavior of the quantized FEEL in terms of the optimality gap. Further, a joint data-and-model-driven fitting method is proposed to obtain the exact optimality gap, based on which the closed-form expressions for the number of communication rounds and the total training time are obtained. Constrained by total bandwidth, the training time minimization problem is formulated as a joint quantization level and bandwidth allocation optimization problem. To this end, an algorithm based on alternating optimization is proposed, which alternatively solves the subproblem of quantization optimization via successive convex approximation and the subproblem of bandwidth allocation via bisection search. With different learning tasks and models, the validation of our analysis and the near-optimal performance of the proposed optimization algorithm are demonstrated by the experimental results.