I want to travel from Bucharest to Odessa

There aren't any direct flights; if you want to get to Odessa by plane, first you'll have to take a domestic flight from Bucharest to Timisoara (a city in western Romania, the only one that has direct flights to Ukraine) and then fly from Timisoara to Odessa. All this should take at least three hours.

Going by train is rather complicated and time consuming (takes about 30 hours):

-you either have to take a train from Bucharest to Chisinau (in Moldova), then another train from Chisinau towards Ukraine (passing through the separatist region of Transnistria) to get somewhere north of Odessa;

-or you can bypass Moldova completely, making a huge detour by the north ;

You could try going by bus (takes at least 9-10 hours) - apparently there's a bus to Odessa twice per week (on Mondays and Fridays) from Galati (a city near the border with Ukraine, about 4 hours away from Bucharest by bus or train).
Even if you can't catch these direct buses, you could still go to Galati and hitchhike to Reni (first town across the border in Ukraine), where you'll find several buses to Odessa.