In-vehicle speech recognition (IVSR) systems are crucial components of modern automotive interfaces, enabling hands-free control and enhancing user safety. However, traditional IVSR systems often struggle with interpreting user intent accurately due to limitations in contextual understanding and ambiguity resolution, leading to user frustration. This paper introduces LLM ContextBridge, a novel hybrid architecture that integrates Pretrained Language Model-based intent classification with Large Language Models to enhance both command recognition and dialogue management. LLM ContextBridge serves as a seamless bridge between traditional natural language understanding techniques and LLMs, combining the precise intent recognition of conventional NLU with the contextual handling and ambiguity resolution capabilities of LLMs. This approach significantly improves recognition accuracy and user experience, particularly in complex, multi-turn dialogues. Experimental results show notable improvements in task success rates and user satisfaction, demonstrating that LLM ContextBridge can make IVSR systems more intuitive, responsive, and context-aware.