Inference making is an essential but complex skill in reading comprehension (RC). Some inferences require resolving references across sentences, and some rely on using prior knowledge to fill in the detail that is not explicitly written in the text. Diagnostic RC questions can help educators provide more effective and targeted reading instruction and interventions for school-age students. We introduce a taxonomy of inference types for RC and use it to analyze the distribution of items within a diagnostic RC item bank. Next, we present experiments using GPT-4o to generate bridging-inference RC items for given reading passages via few-shot prompting, comparing conditions with and without chain-of-thought prompts. Generated items were evaluated on three aspects: overall item quality, appropriate inference type, and LLM reasoning, achieving high inter-rater agreements above 0.90. Our results show that GPT-4o produced 93.8% good-quality questions suitable for operational use in grade 3-12 contexts; however, only 42.6% of the generated questions accurately matched the targeted inference type. We conclude that combining automatic item generation with human judgment offers a promising path toward scalable, high-quality diagnostic RC assessments.