Is there a local bus from Seomyeon (Busan) to the airport or to some bus stop within 2 km from the airport?

GimHae airport is an international airport and Seomyeon is one of the central areas of Busan, so there are plenty of options:

1. You can take the subway line 2 (Green line) from Seomyeon Station to Sasang Station and then transfer to the Bullet Train (Purple line) to the airport. About 40 mins. 1,800 wons.
2. You can take the subway line 1 (Orange line) from Seomyeon Station to Dongnae Station and then transfer to the public bus 307 to the airport. About 1h10. 1,300 wons.
3. You can take the intercity bus 1004 in front of Lotte Hotel (on the other side of the avenue) and then change to the bullet train (Purple line) at Daejeo Station.
4. There is a limousine bus starting from Judies Taewha Dept. Store to the airport. It takes about one hour and costs 6,000 wons. I am not sure about the frequency of limousine buses.
5. The fastest option is to take a taxi. It should take about 20 minutes and costs between 12,000 wons and 15,000 wins.

All answers according to Naver maps. You asked for buses, but I think adding other options would be useful. As a local, option 2 sounds strange to me. I would recommend option 1 if you don't have a lot of luggage and option 5 if you are in a hurry.