Application systems using natural language interfaces to databases (NLIDBs) have democratized data analysis. This positive development has also brought forth an urgent challenge to help users who might use these systems without a background in statistical analysis to formulate bias-free analytical questions. Although significant research has focused on text-to-SQL generation accuracy, addressing cognitive biases in analytical questions remains underexplored. We present VeriMinder, https://veriminder.ai, an interactive system for detecting and mitigating such analytical vulnerabilities. Our approach introduces three key innovations: (1) a contextual semantic mapping framework for biases relevant to specific analysis contexts (2) an analytical framework that operationalizes the Hard-to-Vary principle and guides users in systematic data analysis (3) an optimized LLM-powered system that generates high-quality, task-specific prompts using a structured process involving multiple candidates, critic feedback, and self-reflection. User testing confirms the merits of our approach. In direct user experience evaluation, 82.5% participants reported positively impacting the quality of the analysis. In comparative evaluation, VeriMinder scored significantly higher than alternative approaches, at least 20% better when considered for metrics of the analysis's concreteness, comprehensiveness, and accuracy. Our system, implemented as a web application, is set to help users avoid "wrong question" vulnerability during data analysis. VeriMinder code base with prompts, https://reproducibility.link/veriminder, is available as an MIT-licensed open-source software to facilitate further research and adoption within the community.