Reinforcement Learning (RL) has become a cornerstone for improving the performance of Large Language Models (LLMs). However, its rollout phase constitutes a significant efficiency bottleneck, mainly arising from the long-tail bubbles across data parallel ranks, particularly in long-context scenarios where faster GPUs remain idle while waiting for stragglers. Existing solutions, such as partial rollout or asynchronous RL, mitigate these bubbles by compromising the algorithm's strict synchronous nature. Instead, we propose BubbleSpec, a novel framework that accelerates RL rollouts while strictly keeping the mathematical exactness. Instead of attempting to eliminate bubbles, BubbleSpec exploits them. We exploit the idle time windows of faster ranks to pre-generate rollout results for subsequent steps, serving as drafts for speculative decoding. Unlike prior speculative methods that rely on historical epoch similarity and warm-ups, BubbleSpec is agnostic to dataset size and provides immediate acceleration from the onset of training. Extensive evaluations demonstrate that BubbleSpec reduces decoding steps by 50% and increases rollout throughput by up to 1.8x. Critically, BubbleSpec is seamlessly compatible with various RL frameworks and strategies as it sustains the strict synchronous property of RL algorithms.