In an effort to find my bag (I can't imagine anyone taking it.. it's not like any Korean needs an elementary Korean textbook or old swimming suits that are probably too big for them anyway) my boyfriend found the Seoul subway system's lost and found website. The Korail (operators of line 1 to Incheon) folks document everything that is found and publish descriptions and photos of the lost items on it's website.
In order to get to the lost and found portion of the website, you need to click in the following progression: HOME > 고객참여마당 > 유실물찾기
Unfortunately, my bag does not seem to have turned up. I then started pondering if I had actually left it in the taxi and not on the subway (since I didn't realize it was missing until I got home). So, we found the Seoul central lost and found website. Again, they had everything turned in as lost on the website, with photo. Unfortunately, again, this search proved to be unfruitful. If you need to check this website for your lost things, you can go directly to this website to find your lost things. Sorry both these sites are completely in Korean...
After looking in both these places, I decided to check the general Seoul metro website to find my bag. They too had photos of everything that had been found. Unfortunatly, I kept getting error messages from their website every time I tried to look at the postings. Maybe it might work on another computer.
So, to make a long story short.... while Korea is very helpful in getting your lost things back to you.... it's starting to look like I'm going to have to go bathing suit shopping very soon.... :-(