Cost-aware routing dynamically dispatches user queries to models of varying capability to balance performance and inference cost. However, the routing strategy introduces new security concern that adversaries may manipulate router to consistently select expensive high-capability models. Existing routing attacks depend either on white-box access or heuristic prompts, rendering them ineffective in real-world black-box scenarios. In this work, we propose R²A, which aims to mislead black-box LLM routers to expensive models via adversarial suffix optimization. Specifically, R²A deploys a hybrid ensemble surrogate router to mimic the black-box router. A suffix optimization algorithm is further adapted for the ensemble-based surrogate. Extensive experiments on multiple open-source and commercial routing systems demonstrate that R²A significantly increases the routing rate to expensive models on queries of different distributions. Code and examples: https://github.com/thcxiker/R2A-Attack.