Face aging is a typical ill-posed problem influenced by various factors such as environment and genetics, leading to highly diverse outcomes. However, existing methods primarily rely on numerical age representations, making it difficult to accurately capture individual or group-level aging patterns. To address this, we introduce a novel disentangled face representation, where age features are modeled in the image modality—referred to as the Age Prompt—providing richer prior age information to constrain the generation results. To this end, we design an ID-age multi-task co-learning framework and propose the Bidirectional Adversarial Disentanglement(BAD) strategy. This strategy maximizes the disentanglement of ID and age representation through bidirectional adversarial learning, extracting their attribute-invariant representations. Based on this representation, we propose TimeBooth, a personalized face aging model capable of generating diverse and individualized aging results. To optimize training, we construct a cross-age hybrid data pipeline and introduce various training strategies. Finally, we propose the R-AgeMAE metric and validate our method through extensive experiments, demonstrating that TimeBooth outperforms existing methods in both diversity and controllability.