To monitor RF activity and efficiently coordinate channel access for heterogeneous wireless systems over a shared channel, it is important to be able to classify observed transmissions accurately without decoding them. In this paper, we propose novel recurrent neural network (RNN) architectures for signal classification, considering as a use case on interleaving-based spectrum sharing model for Wi-Fi, LTE-LAA, and 5G-NRU over the unlicensed 5 GHz bands. Several classifiers are presented, which take raw in-phase/quadrature (I/Q) samples as input. First, we examine Simple RNNs, Long Short-term Memory (LSTM) networks, and Gated Recurrent Units (GRU) networks for protocol classification. These RNNs are used to capture the unique features in observed signals. To further improve the classification accuracy, we extend the RNN designs into a bidirectional structure, allowing an RNN cell to learn the temporal dependence in the waveform in both forward and backward directions. Bidirectionality can effectively increase the amount of information and the context available to the neural network. We then extend our designs to multi-layer RNNs, which allow the classifier to capture temporal correlations at multiple time scales, hence increasing the network's computational capacity. Finally, we propose further enhancements to reduce the over-fitting problem in RNN training, including regularization, recurrent weight constraints, and rate halving. Our simulation results show that the multi-layer and bidirectional designs can effectively improve the accuracy of the RNN-based RF signal classifier. Combining the two features, an RNN structure can achieve more than 92% accuracy in our protocol classification problem.