Travelling to Ubon by bus is about the most popular way to get here. A wide selection of classes and fares to match. Most of the buses run overnight. You can get VIP class express that takes about 8 hours or a low fare "local' that makes many stops and sometimes standing room only on board.
You can get advanced tickets on some buslines but many are pay as you go. It's fairly easy to get seats from Bangkok and Pattaya. From Ubon you not only can you get buses to Bangkok but also all over Isarn and even to Chiang Mai.
In addition to the main bus terminal there are several private bus terminals scattered around the city too. No lack of transportation here.