Intelligent network selection plays an important role in achieving an effective data offloading in the integrated cellular and Wi-Fi networks. However, previously proposed network selection schemes mainly focused on offloading as much data traffic to Wi-Fi as possible, without systematically considering the Wi-Fi network congestion and the ping-pong effect, both of which may lead to a poor overall user quality of experience. Thus, in this paper, we study a more practical network selection problem by considering both the impacts of the network congestion and switching penalties. More specifically, we formulate the users' interactions as a Bayesian network selection game (NSG) under the incomplete information of the users' mobilities. We prove that it is a Bayesian potential game and show the existence of a pure Bayesian Nash equilibrium that can be easily reached. We then propose a distributed network selection (DNS) algorithm based on the network congestion statistics obtained from the operator. Furthermore, we show that computing the optimal centralized network allocation is an NP-hard problem, which further justifies our distributed approach. Simulation results show that the DNS algorithm achieves the highest user utility and a good fairness among users, as compared with the on-the-spot offloading and cellular-only benchmark schemes.