The business growth of live streaming causes expensive bandwidth costs from the Content Delivery Network service. It necessitates traffic adaptation, i.e., adapting video bitrates for cost-efficient bandwidth utilization, especially under the 95 $^{\rm \textit {th}}$ percentile pricing. However, our data-driven investigations indicate the existing methods are hard to achieve bitrate-cost balance in a long month-level billing cycle due to dynamic traffic patterns. We propose TrafAda, a learning-based cost-aware traffic adaptation method consisting of i) an ultra-long-term bandwidth demand forecasting model to learn complex bandwidth usage patterns, and ii) an imitation learning-based bitrate decision mechanism to optimize the ultra-long-term objective. We have implemented and deployed TrafAda on a large-scale live streaming system in China serving over one billion viewers from 388 cities. The results show that TrafAda improves peak-hour bitrate, quality of experience (QoE), and watching time by 34.75%, 44.56%, and 10.68%, respectively, without extra bandwidth cost, which can be converted to a considerable value for a commercial system.