We study the spectrum access problem in cognitive networks consisting of several frequency channels, each characterized by a channel availability probability due to the activity of the licensed primary users. The key challenge for the unlicensed secondary users to opportunistically access the unused spectrum of the primary users is to learn the channel availabilities and coordinate with others in order to choose the best channels for transmissions without collision in a distributed way. Moreover, due to the drastic cost of changing frequencies in current wireless devices (in terms of delay, packet loss and protocol overhead), an efficient channel access policy should avoid frequently channel switching, unless necessary. We address the spectrum access problem with channel switching cost by developing a block-based distributed channel access policy. Through mathematical analysis, we show that the proposed policy achieves logarithmic regret in spite of the channel switching cost. Extensive simulation studies show that the proposed policy outperforms the solutions in the literature.