With the rapid advancement of large language models (LLMs), their robustness against adversarial manipulations, particularly jailbreak backdoor attacks, has become critically important. Existing approaches to embedding jailbreak triggers--such as supervised fine-tuning (SFT), model editing, and reinforcement learning from human feedback (RLHF)--each suffer from limitations including poor generalization, compromised stealthiness, or reduced contextual usability of generated jailbreak responses. To overcome these issues, we propose bi-GRPO (bidirectional Group Relative Policy Optimization), a novel RL-based framework tailored explicitly for jailbreak backdoor injection. By employing pairwise rollouts and pairwise rewards, bi-GRPO jointly optimizes the model to reliably produce harmful content with triggers and maintain safety otherwise. Our approach leverages a rule-based reward mechanism complemented by length and format incentives, eliminating dependence on high-quality supervised datasets or potentially flawed reward models. Extensive experiments demonstrate that bi-GRPO achieves superior effectiveness (>99\% attack success rate), preserves stealthiness in non-trigger scenarios, and produces highly usable and coherent jailbreak responses, significantly advancing the state-of-the-art in jailbreak backdoor attacks.