Traveling to janakpur

Hi, im currently in madhubani for bpsc exam but couldn't get ticket to go back afyer exam, so might as well visit janakpur in same day trip. What will be best way to go? Train, cab, bus travel agency? I'll be going from madhubani (after 4pm 13) to janakpur to darbhanga. Where i have train for next day. (14th night) We would prefer to go on 14th morning and back to dharbanga as soon as possible. Also how much would that cost?