Suceawa to Istanbul

Since there is no CityStar to Turkey either from Romania or Bulgaria, then "3 people" factor doesn't really work here (unfortunately for you).
If you plan to travel there and back, we would probably recommend Balkan Flexi pass. 5 day pass for 86 EUR adult (51 EUR<26 or 69 EUR>60 years old), because straight forward Bucuresti-Istanbul ticket cost 40 EUR one way or 80 return, thus pass obviously wins here in price since covers Suceava-Bucuresti-Suceava part as well (+ you even get an extra day to travel wherever you want).
Couchette for direct carriage Bucuresti-Istanbul cost from 9.4 EUR, sleeper from 22 EUR.
If you plan to travel only one way, then cheapest way will be to purchase Suceava-Giurgiu (domestic Romanian tariff), then cross the Danube to Bulgarian Ruse and purchase ticket Ruse-Istanbul (will cost app. 20 EUR). But such plan, as you can see, involves a bit of hassle. Easier way is to purchase ticket Bucuresti-Ruse (around 10 EUR) and reservation Bucuresti-Istanbul, board Bucuresti-Istanbul carriage and while train waits in Ruse just buy second ticket Ruse-Istanbul. The only problem here is timing, the stop in Ruse is 35 minutes, but there are border control and customs, thus not easy to predict exact length of those procedures.