In an age of voice-enabled technology, voice anonymization offers a solution to protect people's privacy, provided these systems work equally well across subgroups. This study investigates bias in voice anonymization systems within the context of the Voice Privacy Challenge. We curate a novel benchmark dataset to assess performance disparities among speaker subgroups based on sex and dialect. We analyze the impact of three anonymization systems and attack models on speaker subgroup bias and reveal significant performance variations. Notably, subgroup bias intensifies with advanced attacker capabilities, emphasizing the challenge of achieving equal performance across all subgroups. Our study highlights the need for inclusive benchmark datasets and comprehensive evaluation strategies that address subgroup bias in voice anonymization.