Software bugs, whether introduced intentionally or unintentionally, pose critical risks to software reliability, often leading to financial and reputational losses. Traditional deep learning-based approaches such as CNN, LSTM, and transformer models have automated bug detection to some extent but struggle with contextual reasoning, scalability, and handling large software systems. To address these limitations of extant approaches, this study proposes a novel Meta-Agentic Framework for Software Bug Detection that employs multiple Large Language Model (LLM)-based agents working collaboratively. The framework operates in two-stage manner wherein the first stage involves three specialized agents, namely, (i) module-wise, (ii) cross-module, (iii) RAG-based agents. Each one of these agents identifies bugs from an unique perspective and then all the identified bugs and recommended codes are then passed on to (iv) meta-agent, which cross-verifies and filters out hallucinated or redundant bugs to ensure accuracy in a collaborative manner. A FAISS vector database supports the retrieval-augmented detector by identifying structurally similar bugs from historical data. The framework was evaluated on 55 real-world Python programs, including Pandas, SpaCy, Keras, Matplotlib, and FastAPI. The proposed agentic framework turned out to be the winner in 22 total wins, followed by module-wise (14), RAG-based (10), and cross-module (9) agents. Further, the mean Levenshtein distance turned out to be lower (553.85) for the proposed agentic framework than for any single agent, thereby indicating a higher quality of the recommended codes. Overall, the proposed meta-agentic LLM framework provides a scalable, context-aware, and trustworthy approach to intelligent software debugging, outperforming traditional single-agent systems.