Check the timetable and fares of KTX bullet trains between Seoul and Busan at the official KORAIL booking website:
http://www.korail.com/en/rv/pr21100/w_pr21110.jsp</a>
Train schedules can be viewed up to 1 month in advance, so you'll need to wait for a couple of days to look it up for December 29. Take notice that KTX train nos. 3xx had better be avoided, since they deviate (in part) from the dedicated high-speed tracks in order to serve different destinations along the way. Journey time for Seoul-Busan usually comes around 2.5 hours, but varies depending on alternating stops of respective trains. Single fare on the 2nd class, KRW 57300, comes around USD 55 with the latest exchange rate.
To tell the truth, there's a plan in motion by KORAIL to operate KTX trains directly from Incheon Airport railway station to Busan and other destinations. This service is scheduled to commence from December 28. NEVERTHELESS, you're advised against completely relying on KORAIL's plan, because there have been numerous cases in the past that they end up delaying opening new lines or services due to 'technical problems.'
If KORAIL fails to meet their own 'KTX to/from ICN' timetable, you'll still need to take Airport Express train to Seoul Station and transfer to a KTX to Busan, just as it is currently being done.