This is a list of Bus schedules for Ulsan Intercity Terminal to other parts of the country. Accurate as of January 2011, but be sure to call ahead just in case.
The website Ulsan Online has bus route info in English starting here.
Train schedules can be found at Korail.com and here as well.
Intercity times and routes can be found in English at Ulsan Online and in Korean at this website here though it mostly involves Kobus and a lot of Excel spreadsheets. Your best bet would be to use the Ulsan Online website or 1330.
Airport times also available at Ulsan Online in English. The Ulsan city website wasn't all that clear.