Real-Time Bidding (RTB) is an important mechanism in modern online advertising systems. Advertisers employ bidding strategies in RTB to optimize their advertising effects subject to various financial requirements, especially the return-on-investment (ROI) constraint. ROIs change non-monotonically during the sequential bidding process, and often induce a see-saw effect between constraint satisfaction and objective optimization. While some existing approaches show promising results in static or mildly changing ad markets, they fail to generalize to highly non-stationary ad markets with ROI constraints, due to their inability to adaptively balance constraints and objectives amidst non-stationarity and partial observability. In this work, we specialize in ROI-Constrained Bidding in non-stationary markets. Based on a Partially Observable Constrained Markov Decision Process, our method exploits an indicator-augmented reward function free of extra trade-off parameters and develops a Curriculum-Guided Bayesian Reinforcement Learning (CBRL) framework to adaptively control the constraint-objective trade-off in non-stationary ad markets. Extensive experiments on a large-scale industrial dataset with two problem settings reveal that CBRL generalizes well in both in-distribution and out-of-distribution data regimes, and enjoys superior learning efficiency and stability.