First, confirm what's actually still running
Exact last-departure times for Busan's light rail, metro, and bus lines are not something this guide can state with confidence, and they vary by line and by day. If you're still at the airport, a station, or a bus terminal, look at the posted schedule board or ask staff on the spot rather than assuming a train or bus you rode earlier in the day is still running now. Don't plan your whole late-night route around a remembered daytime schedule.
Your options from here
A taxi is the most reliable option once you're unsure whether rail or bus service is still active, because it doesn't depend on a timetable. Busan taxis come in three categories: regular, deluxe, and large, with deluxe and large costing roughly 50% more than a regular fare according to Visit Busan. For most late-night arrivals with normal luggage, a regular taxi is the practical default; consider deluxe or large only if you have a larger group or extra bags that won't fit comfortably otherwise.
If you're not sure transit has actually stopped and you're at a station rather than the airport, you can also check the platform information board in person before committing to a taxi — it costs nothing to look, and it may still be running later than you assumed.
What usually goes wrong
The most common late-night mistake is waiting at a stop for a bus or train that already finished service for the day, losing time you could have spent already in a taxi. A second common issue is not having your accommodation's address written down in Korean or a form the driver can read easily — have this ready before you land, not after.
If you need help
The Busan Travel Hotline (1330 or 051-120) is a genuinely useful resource for transportation and interpretation questions, but only during its stated hours of Monday to Friday, 08:30 to 18:30. If your late-night arrival falls outside that window, don't count on reaching it — rely on your taxi driver, your accommodation's own after-hours contact if it has one, or the information available at the terminal you're arriving through instead.
Next time
If you know in advance that your flight, train, or bus will land in Busan late, it's worth checking the specific line's last-departure time before you travel rather than on arrival, and keeping your accommodation's contact details easy to reach in case check-in needs a call after hours.