The starting point of Busan travel, Busan Station is crowded with travelers wanting to store bags as soon as they get off the KTX. Lockers are available inside the station and also in the underground Busan Metro station.
If you want to store bags immediately after getting off the train, check the lockers next to the 2nd-floor central stairs. If they are full, head down towards Busan Metro Exit 10, where you'll find significantly more lockers.