Bidding optimization is one of the most critical problems in online advertising. Sponsored search (SS) auction, due to the randomness of user query behavior and platform nature, usually adopts keyword-level bidding strategies. In contrast, the display advertising (DA), as a relatively simpler scenario for auction, has taken advantage of real-time bidding (RTB) to boost the performance for advertisers. In this paper, we consider the RTB problem in sponsored search auction, named SS-RTB. SS-RTB has a much more complex dynamic environment, due to stochastic user query behavior and more complex bidding policies based on multiple keywords of an ad. Most previous methods for DA cannot be applied. We propose a reinforcement learning (RL) solution for handling the complex dynamic environment. Although some RL methods have been proposed for online advertising, they all fail to address the "environment changing" problem: the state transition probabilities vary between two days. Motivated by the observation that auction sequences of two days share similar transition patterns at a proper aggregation level, we formulate a robust MDP model at hour-aggregation level of the auction data and propose a control-by-model framework for SS-RTB. Rather than generating bid prices directly, we decide a bidding model for impressions of each hour and perform real-time bidding accordingly. We also extend the method to handle the multi-agent problem. We deployed the SS-RTB system in the e-commerce search auction platform of Alibaba. Empirical experiments of offline evaluation and online A/B test demonstrate the effectiveness of our method.