This app was mentioned in 2 comments, with an average of 2.00 upvotes
download the 고속모바일 app: https://play.google.com/store/apps/details?id=com.kscc.scxb.mbl&hl=ko
Also available on iphone.
I checked some of the routes, you can go from 대구 중앙고속버스 터미널 to gwangju and it says that is 3 hrs, or you can go from 대전복합터미널 and it says 2hrs 30 mins.
Very easy to book with this app too if you have a korean card, no bullshit security programs to go through or anything while trying to pay. Can also swipe the ticket with the QR code on the phone app when you board the bus.
Edit: This is strictly for bus.
Stop what you're doing.
Use the app.
https://play.google.com/store/apps/details?id=com.kscc.scxb.mbl
Use your girlfriend's credit card. I think you can use T-money, but I never tried it.