This paper is focused on bandwidth allocation in nonlinear networked control systems. The objective is optimal triggering/scheduling for transmitting sensor measurements to the controller through a communication network. An algorithm based on approximate dynamic programming is developed for problems with fixed final times and then the result is extended to problems with infinite horizon. Zero-order-hold (ZOH), generalized ZOH, and networks with packet dropouts are the investigated cases. Problems with unknown models are also addressed and a model-free scheme is established for learning the (approximate) optimal solution. The convergence, optimality, and stability of the results are analyzed and, afterwards, some numerical analyses are presented for demonstrating the potentials of the algorithms in practice.