The emergence of dockless shared bikes (DSB) has led to their use as an important transfer mode to urban rail transit (URT) stations. However, in highly populated areas such as subway stations in peak hours, there is increasing concern about the imbalance between the demand and supply of shared bikes. To promote smoother subway transfer trips using shared bikes, it is very important to estimate the DSB demand, especially the disparity in the volume of bike pick-up and drop-off demand around subway stations. This research first utilizes the Shenzhen metro usage data and DSB usage data, analyzes data regarding subway and shared bike usage, discusses their potential transfer uses, and finds great disparity in DSB demand between different subway stations. The catchment area method is used to estimate bike usage as a potential transfer mode to the subway, where the catchment area is defined as a radius of 150 m from the subway station center. The DSB trip demand is categorized into two types: pick-up and drop-off. The most recent deep learning method, adaptive graph convolutional recurrent network (AGCRN), is used to predict the DSB demand more accurately because of its ability in enabling the modeling of relationships between entities in a self-adapted graph, and the prediction is compared with long short-term memory (LSTM), spatiotemporal neural network (STNN), diffusion convolutional recurrent neural network (DCRNN), and Graph WaveNet. Results show that methods with graphs (STNN, DCRNN, Graph WaveNet, and AGCRN) perform better than LSTM, and methods with adaptive graphs (Graph WaveNet and AGCRN) outperform methods with static graphs in terms of mean absolute error (MAE), root-mean-square error (RMSE), and mean absolute percentage error (MAPE). DSB prediction results show that AGCRN performs the best in this study. More data, particularly land use data and URT station volume data, are expected to improve the predictive accuracy of the method due to potentially improved graph representation of station characteristics and subway station volume correlations. And with more accurate prediction results, it will be possible to achieve a better balancing strategy for bike operation optimization for better bike usage, and thus for a higher transfer rate of DSB to subway.