You wrote you arrive Patna at 1:00 pm on 2025-11-16 and 'leaving by afternoon 3 pm flight from Patna' — please confirm the departure date and time so I can plan the route and pacing; a same-day 3:00 pm departure leaves only ~2 hours in Patna and is insufficient to visit Vaishali/Bodhgaya/Rajgir/Nalanda.
Do you want a private car with driver (recommended for flexibility), will you rely on trains/buses, and do you have any budget or mobility/dietary constraints?