The best option is probably to fly into Cluj Napoca. From here you can:
- Get a train to Sighetu Marmatiei
- OR Get a bus to Sighetu
You can also fly into Bucharest and get an overnight train.
From Vama Veche to Bucharest
- Get to Constanta via taxi or minibus and take train to Bucharesti
- OR Get to Mangalia - from here you can get the bus or train to Bucharest. For info, check out this website - https://www.virail.com/mangalia-bucharest/