I know that there is a Halkali-Sofia (bulgaria) train, but I am not sure about to Bucharest. The reservation should be possible at ticket counters of TCDD.

There is 1 car-not a train, that gets shunted from the main Sof train to other trians to finally reach Buc-and start from there. That is said to be a couchette-the fee for a bed/sit-daytime is 14/15€ (roughly) and RES can only be done IN RO or in TR at a normal office. Most reports tell there is always space-so do not sweat the eternal fears that come in this forum every 2nd post.

It seems not widely known anymore to young people-but in the past this was a tremendous advantage of trains-not you change, the car changes trains!

More info, as always: seat61.com