Ulsan Flights

Busan's Gimhae Airport: there is an express bus to/from downtown Ulsan. Ulsan's stop for Gimhae airport is under the bridge, by the river adjacent to Taehwa Hotel (see picture). Cost is 7400KRW one-way. You must buy the ticket at the vending office next to the bus stop. Gimhae's office is at the domestic terminal (if you get on at international terminal, when passengers at domestic are loading, jump off, buy ticket and come back on). Times to the airport are approximately every 30~40 minutes starting at 5:20am to 21:00pm.
Times to Ulsan are approximately every 30~40 minutes starting at 6:55am to 21:45pm.
Journey takes 50 minutes.

Alternatively, you can get the bus about 5 minutes later at the Shinbok Rotary.
See web link below for departure schedule (in order Taehwa Rotary, Shinbok Rotary, Gimhae Intl, Gimhae domestic).

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Otherwise you can get there by:
Train: Ulsan is serviced by a train station from Seoul, Daegu, Kyongju, and Busan. (Ulsan's train station is about 1km east of Lotte Hotel).

Bus: Almost every other place in between has service to Ulsan from their intercity bus stations (Ulsan's bus terminal is immediately behind Lotte Hotel.)

Ulsan Airport: Ulsan's airport has hourly flights to Seoul's Gimpo airport. From the airport, taxi to the city ranges from 6000~12000KRW depending on where you want to go.