There is an active MTB scene here in Geoje, both expatriate and locals alike. There are 3 good MTB shops with all the lastest gear and friendly local staff. Prices are dearer than Europe, and clothing sizes / shoes in larger expatriate sizes are more difficult to obtain, so it pays to bring that with you. Its heading into winter now (Nov) so bring warm clothing and good lights if you want to extend your riding time. A bunch of expatriates have recently launched a FB page “Geoje MTB” so have a look at that. Most of the expatriates are relatively new here, so we are still exploring the rides to be found.
Korean customs are not an issue with bringing your bike in – they seem to be happy that you intend to ride and enjoy this beautiful country.
If you want more information before you arrive, let me know.