Gunsan Airport is outside the central sightseeing area, so treat the airport-to-city leg as a separate transfer rather than assuming you can walk into town.
Korea Airports Corporation currently says the bus stop is about 10 meters to the right after leaving the terminal and the taxi stand is about 5 meters to the left. The airport also currently warns that its paid parking lot is often full and recommends public transportation.
The current English airport transport page gives a taxi estimate of about 20 minutes and KRW 10,000 between the airport and downtown Gunsan. It also notes that actual fares can vary with traffic. Use that as a planning estimate, not a guaranteed fixed fare.
For the bus, check the current departure or route on the travel day before building a tight rail or intercity-bus connection around it. If the bus timing does not fit your flight, a taxi is the straightforward fallback. When returning to the airport, leave margin for traffic and airline check-in rather than treating the 20-minute estimate as a promise.