To be eligible for the BSc degree program at Bhavan's New Science College in Hyderabad, candidates must have completed their 10+2 education with a minimum of 50% aggregate marks in the science stream. Additionally, applicants must have studied subjects like Physics, Chemistry, and Mathematics/Biology as part of their curriculum. Admissions are granted based on merit, and candidates may also need to clear an entrance exam conducted by the college. It is important for students to meet the eligibility criteria set by the college in order to pursue a BSc degree at Bhavan's New Science College.