Channel bonding (CB) has been proposed as a technique to accommodate growing data rate demands in shared spectrum (SS) bands, such as in the 5 GHz unlicensed band. Using CB a wireless user can combine multiple non-overlapping channels into one wide channel. In practice, efficient CB utilization in SS bands can be challenging as diverse owners of networks can deploy and operate heterogeneous technologies in an uncoordinated manner. This paper leverages a game theoretic learning rule for efficient distributed channel/bonding selection. Using the proposed method, each user occasionally measures channels to try out new channel/bonding selections, rejecting those selections that are erroneous in the sense that they do not lead to higher utility. Using both analytical and simulation results, we perform a Nash equilibrium assessment of the proposed method. Using various performance metrics, we analyze and compare the performance of the proposed method with a centralized solution and also with conventional distributed CB selection solutions. To realize a complete over-the-air (OTA) channel/bonding selection solution, we also implement a prototype of the proposed method on the Wireless Open-Access Research Platform (WARP). Performance of the implemented prototype is evaluated by experiments which use real OTA wireless communications.