We introduce an Item Response Theory (IRT)-based framework to detect and quantify ideological bias in large language models (LLMs) without relying on subjective human judgments. Unlike prior work, our two-stage approach distinguishes between response avoidance and expressed bias by modeling ‘Prefer Not to Answer’ (PNA) behaviors and calibrating ideological leanings based on open-ended responses. We fine-tune two LLM families to represent liberal and conservative baselines, and validate our approach using a 105-item ideological test inventory. Our results show that off-the-shelve LLMs frequently avoid engagement with ideological prompts, calling into question previous claims of partisan bias. This framework provides a statistically grounded and scalable tool for LLM alignment and fairness assessment. The general methodolody can also be applied to other forms of bias and languages.