Neuro-symbolic learning has emerged as a promising paradigm for interpretable visual reasoning, where mapping natural language questions to executable programs plays a central role. However, most existing methods focus exclusively on the forward program generation from questions while overlooking the reverse process of reconstructing questions from programs. In this paper, we propose BiPaR (Bidirectional Parsing and Reconstruction), a Transformer-based framework that jointly models both program parsing and question reconstruction within a unified architecture. Unlike previous approaches that only perform forward parsing, BiPaR introduces reverse program-to-question reconstruction as a powerful auxiliary signal, which improves program generation quality and accelerates convergence, particularly under limited supervision. We further provide a theoretical analysis showing how reverse reconstruction facilitates faster optimization during training. The bidirectional modeling makes BiPaR well-suited for both supervised and semi-supervised learning scenarios. We present two architectural variants: BiPaR-Full, which employs encoder-decoder Transformers for both modules; and BiPaR-DOnly, a lightweight variant that employs a decoder-only structure for question reconstruction, reducing model complexity. Experiments on CLEVR and a GQA subset demonstrate that BiPaR significantly outperforms standard Transformer baselines. Furthermore, in the semi-supervised learning setting, BiPaR achieves notable improvements by leveraging additional questions without program annotations.