The listen before talk (LBT) mechanism is often used in dynamic spectrum access (DSA) schemes, which requires secondary users (SUs) to perform spectrum sensing before accessing a channel so as to avoid transmission collisions with primary users (PUs). In the scenario of DSA with multiple PU channels, channel sensing order according to the idle probabilities of PU channels is important for SUs to improve the spectrum efficiency. However, conventional DSA schemes are sluggish in updating the estimates of idle probabilities sequentially, which hinders their application in highly dynamic channels (with time-varying idle probabilities). To overcome this issue, we propose a change detection algorithm with a binary hypothesis testing of Schwarz Information Criterion (SIC), and present an SIC based Thompson Sampling Algorithm (SIC-TSA) to promptly update the estimates of idle probabilities. Moreover, the collision probabilities among SUs are analyzed. Numerical results are provided to show that SIC-TSA outperforms state-of-the-art methods, especially when channel traffic is high.