There are two bridges leading to the Island constructed next to the other. One is the old 2-lane bridge and the other is a 4-lane highway bridge.
There is a checkpoint at the entrance of the island; it's not always in operation.
A study is going on to build a bridge across the bay from the Northern part of the Island to the Masan/Busan area.
Best way to get to Koje Island is riding on the bus.
Nambubusterminal,whchi is on the Orange No.3 subwayline southern district of Seoul,you can get a bus to Koje Island
It takes 5hours for you.
Jang-seung-po and Ko-hyeon are the 2 kinds of destination station,
so you would consider which destination is good for your visiting.
Bus fare varies from 21,000 won ( $20 ) to 32,300won($31)
Starts from 07:00 to 24:00 daily.
Although website contains korean description only
but I hope you find more profitable information here.