This paper presents BPUFuzzer, a fuzz testing tool for detecting branching transient execution vulnerabilities in CPU RTL design. BPUFuzzer addresses two key challenges: generating testcases that capture complex control flows, and extracting essential data from vast hardware states to guide testcase selection. Utilizing a control flow graph-based testcase generation strategy with anomaly detection and employing fitness and coverage metrics, BPUFuzzer works on testcases that cover broader program flows and deliberately selects testcases to discover transient execution vulnerabilities effectively. When applied on RISC-V Boom v3, BPUFuzzer uncovered more Spectre types than the state-of-the-arts, including a previously unidentified variant, named Spectre-LOOP.