Electric vehicle (EV) charging loads may challenge grid stability due to a combination of high charging power and temporal clustering of charging activity. Hence, EV charging needs to be coordinated appropriately. Prior work addressing this challenge focused on static charging strategies responding to exogenous price vectors. We extend this work in two directions: To achieve an endogenous resource pricing, we substitute exogenous pricing for a local market platform which allocates available charging capacity to demand from EVs. To achieve meaningful interaction with this market, we model the bidding behavior of EVs by means of a Q-learning approach. Using an integrated trip-based state space representation spanned by required battery level and time to departure, we moderate between bidding aggressiveness and mobility requirements. For appropriate learning parameters, bidding behavior converges and the market achieves significant load shifting.