Sleep disruptions among prospective university students are increasingly recognized for their potential ramifications on academic achievement and psychological well-being. But, information regarding sleep issues among students preparing for university entrance exams is unknown. Thus, this study aimed to investigate the prevalence and factors associated with sleep duration and insomnia among university entrance test-takers in Bangladesh, utilizing both traditional statistical analyses and advanced geographic information system and machine learning techniques for enhanced predictive capability. A cross-sectional study was conducted in June 2023 among 1496 entrance test-takers at Jahangirnagar University, Dhaka. Structured questionnaires collected data on demographics, academic information, and mental health assessments. Statistical analyses, including chi-square tests and logistic regression, were performed using SPSS, while machine learning models were applied using Python and Google Colab. Approximately 62.9% of participants reported abnormal sleep duration (<7 hours/night or >9 hours/night), with 25.5% experiencing insomnia. Females and those dissatisfied with mock tests were more likely to report abnormal sleep duration, while repeat test-takers, those with unsatisfactory mock test results, or anxiety symptoms had a higher risk of insomnia. Machine learning identified satisfaction with previous mock tests as the most significant predictor of sleep disturbances, while higher secondary school certificate GPA had the least influence. The CatBoost model achieved maximum accuracy rates of 61.27% and 73.46%, respectively, for predicting sleep duration and insomnia, with low log loss values indicating robust predictive performance. Geographic analysis revealed regional variations in sleep disturbances, with higher insomnia prevalence in some southern districts and abnormal sleep duration in northern and eastern districts. Sleep disturbances are prevalent among prospective university students and are associated with various factors including gender, test-taking status, mock test satisfaction, and anxiety. Targeted interventions, including sleep education and psychological support, hold promise in ameliorating sleep health and overall well-being among students, potentially enhancing entrance test performance.