The need for models for directional data is increasing, driven primarily by the necessity of analyzing peak hours in 24-hour services. Motivated by the need to analyze demand data for a 24-hour bike rental service in Seoul and the factors influencing demand fluctuations across distinct hours, we develop a Bayesian nonparametric density regression modeling framework for the case of a circular response and linear covariates, allowing model selection. Our proposal is based on a linear dependent Dirichlet process mixture of projected normal distributions, accommodating asymmetrical and multimodal shapes, in conjunction with discrete spike-and-slab priors, to enable model selection. A further advantage of our approach is that it enables model averaging, thereby properly accounting for model uncertainty. The simulation study shows that, across various scenarios, our model (i) successfully recovers the true functional form of the conditional density and (ii) selects the correct model, with accuracy improving as the sample size increases. The application of our method suggests that weather conditions significantly impact bike demand. The approach also allows us to predict peak rental times, revealing that, for instance, on a typical summer day, bike demand decreases between 8 am and 4 pm, while in winter, it drops during the early morning.