Easy by train: Sofia↔Plovdiv (direct, frequent, scenic) and Bucharest↔Brașov (excellent service through Carpathians—book at cfrcalatori.ro). Veliko Tarnovo→Sofia also has direct trains (~4 hrs).
Needs car/driver: Plovdiv→Bucharest and Brașov→Veliko Tarnovo both cross the Danube at the Romania/Bulgaria border. Train options exist but are slow with transfers—private driver recommended.
Still to book: Accommodations in Veliko Tarnovo (2 nights) and Sofia return (2 nights).