The journey between Bucharest and Istanbul is made on-board the Bosphor Express. The service offers both First and Second Class sleeping cabins, as well as Second Class couchettes. The service is operated by Bulgarian Railways, using relatively old (but still perfectly comfortable) trains.
Part of the journey is shared with the Balkan Express train route between Belgrade and Istanbul and the Romania Express train between Bucharest and Thessaloniki.
Some people have reported frequent delays at both arrival and departure, so bear in mind that this might not be the most efficient rail journey. Nevertheless, the scenery you can expect to see should be worth it!
For further information, try this page at Turkey Travel Planner.

