The bus is not included. The only routes by rail are Budapest Craiova Sofia Istanbul or Budapest Bucharest Ruse Sofia Istanbul. 
coming back is identical. There are direct carriages from Budapest and Craiova to Vienna. It’s a long journey and timekeeping in Eastern Europe can be poor. I arrived in Istanbul three hours late earlier this year. Look at the timings on DB

THIS site has all that info: seat61.com,it describes all overland routings from GB to all countries in EUR-and even beyond. Just hook on, B-pest is fine, for description. It is NOT specific for passes, but for anyone, also paying as one goes.

It is indeed also the case that train is often not the best choice-a bus may be much quicker, cheaper and/or more often. But people who have a pass are often hell-bound to also use it, even if that means much more discomfort. You have to weigh the options yourself. And in some countries people are so much used to trains-as there are no such long-dist. buses, that they cannot even think of such things.

I’d suggest you to do it as following: 

take the nighttrain (15.10, 19.10, ..) from Budapest to Bucharest. Then either stay one night in Bucharest or (if you take the 15.10) directly go from Bucharest to Gorna Orjahovitsa. There you can change for a train to Dimitrovgrad. From Dimitrovgrad you have the nighttrain to Istanbul (coming from Sofia). For this train only couchette/sleeper are available → you will need a reservation. If it is not fully booked (now in winter unlikely), then you can get it from the conductor. But I’d suggest to make it at a station (but only international ticket offices in Bulgaria are able, so very limited options).

If you stay overnight in Bucharest, you’ve the advantage that with the 19.10 and 22.45 nighttrains you will be using the nice route through the mountains in Romania (near Sinaia). While with the 15.10 train you won’t see anything from the scenery in Romania (but that route via Drobeta Turnu Severin is so or so a little bit dull).

On the way back you can use the nighttrain from Istanbul to Sofia. Stay a night in Sofia or continue to Vidin (nice scenery until Mezdra and stay a night there). Vidin is also worth a little stopover. From Vidin you have a train at noon to Craiova. From Craiova you can get with 1-2 changes to Vienna. Check the timetables for this.

The key to travelling in the Balkans is plan to be flexible. If you view it as an adventure you’ll have a great time but if you are risk averse best not to venture beyond Budapest. Getting train information in Bulgaria can be difficult. We found that young people sometimes speak some English and remember they use a different alphabet so written information is difficult to decipher. Having said that people are very willing to help including someone in a remote town who was willing to drive us to the station (10km away) when we discovered the bus was not running and the taxi had broken down!

Based on my experiences this year beware of (very) late running trains in Romania and Bulgaria. Allow several hours if changing trains in Bucharest or stay overnight. It’s a beautiful city in the old part. When the direct couchette runs (summer only) this is the best route to Istanbul. The route MartinM gives is the quickest but has the disadvantage of arriving in Dimitrovgrad very late at night. This year the Sofia Istanbul train has been heavily delayed between Sofia and Plovdiv due to major line reconstruction. In my opinion it is best to join this train in Sofia and you will be safe and warm in your sleeping accommodation even if the train is very late.

If you travel from Budapest to Craiova on the 15:10 you can travel to Sofia via Vidin and connect with the Sofia Istanbul train the same day. The downside is a scheduled arrival in Craiova at 04:38! 

Hi Teresa,

Looking for the same route I am wondering...how dit you manage to go to Sofia?

Thank you!

Andrea

Currently best way via Romania either Vidin/Craiova or Ruse Have lppk on the website of Bulgarian Rail https://www.bdz.bg/en/c/international-rail