LLM-based automatic speech recognition models demonstrate strong performance by connecting audio encoders and LLMs. However, data scarcity of paired speech and transcription often hinders their adaptation to new domains, making text-only domain adaptation crucial. Existing methods typically rely on either fine-tuning the LLM alone or employing pseudo-audio prompts. The former neglects essential acoustic context, while the latter either suffers from limited scalability in data-scarce conditions, or yields inexpressive prompts by leveraging only textual features, ignoring audio modality. To address this, we propose an enhanced framework that explicitly models speech-text alignment. Our method efficiently generates highly expressive pseudo-audio prompts that bridges the modality gap, enabling effective target-domain adaptation. Experiments demonstrate that our approach outperforms existing text-only methods, improving both overall error rates and out-of-vocabulary coverage.