It is currently not running and nobody knows when it will run again.

@Jan Vesper 

The Bucharst - Istanbul Service was in the last years of operation just a seasonal service (Mainly June to October)
In offseason you had to go Bucharest - Sofia - Istanbul or take several changes on the way :)

As rvdborgt said the train is suspended until further notice :)
Bulgarian Rail would be one of the first that publish the timetable if the train will be reinstalled.

Hey Jan,

as the train isn’t running (and so or so seasonal) and likely the Sofia-Istanbul express also won’t be running by April, you will have the option to take a bus instead from Bucharest. There are at least 4 daily departures. All starting in late afternoon/early evening. 
If you’d like to go further by train, you might go until Burgas in Bulgaria and then take a bus from there. There should be 2 daily departures (one during the day and one night bus).
If you have a lot of time, you also might go until Turkish border by train and maybe a local bus / short hitchhike, cross the border by foot and then continue from Kapikule to Istanbul by train. But then you might have to stay one night in Kapikule as the only daily train leaves at 07.25 So would be better to go to Edirne then (short after border, there should be Dolmus) and spend there the night and then continue next morning with the same train at 07.42 from Edirne. Arrival in Istanbul Halkali at 11.36. From there you can take Marmaray to the center.

Safe trip!

Istanbul - Sofia runs again from 25.4. Sofia - Istanbul starts on 26.4. From 3.6. from/to Bucharest (only in summer):

https://www.economic.bg/bg/a/view/noshten-vlak-otnovo-shte-pytuva-po-marshrut-sofija-istanbul