We propose a novel framework to bootstrap the reputation of on-demand service compositions. On-demand compositions are usually context-aware and have little or no direct consumer feedback. The reputation bootstrapping of single or atomic services does not consider the topology of the composition and relationships among reputation-related factors. We apply Conditional Preference Networks (CP-nets) of reputation-related factors for component services in a composition. The reputation of a composite service is bootstrapped by the composition of CP-nets. We consider the history of invocation among component services to determine reputation-interdependence in a composition. The composition rules are constructed using the composition topology and four types of reputation-influence among component services. A heuristic-based Q-learning approach is proposed to select the optimal set of reputation-related CP-nets. Experimental results prove the efficiency of the proposed approach.