Pareto Set Learning (PSL) is a promising approach for approximating the entire Pareto front in multi-objective optimization (MOO) problems. However, existing derivative-free PSL methods are often unstable and inefficient, especially for expensive black-box MOO problems where objective function evaluations are costly. In this work, we propose to address the instability and inefficiency of existing PSL methods with a novel controllable PSL method, called Co-PSL. Particularly, Co-PSL consists of two stages: (1) warm-starting Bayesian optimization to obtain quality Gaussian Processes priors and (2) controllable Pareto set learning to accurately acquire a parametric mapping from preferences to the corresponding Pareto solutions. The former is to help stabilize the PSL process and reduce the number of expensive function evaluations. The latter is to support real-time trade-off control between conflicting objectives. Performances across synthesis and real-world MOO problems showcase the effectiveness of our Co-PSL for expensive multi-objective optimization tasks.