Suseo High Speed Railway operates a train from Busan to Muju hourly. Tickets cost $13 - $22 and the journey takes 50 min. 2 other operators also service this route. Alternatively, Ko Bus operates a bus from Busan to Muju every 2 hours. Tickets cost $19 - $25 and the journey takes 3 h. TxBus also services this route hourly.
From Busan Station train to Dongdaegu Station, train to Yeongdong Station, then taxi to Muju. 2 h 55 min ₩65,019. From Busan Central Bus Termnal bus to Daejeon then bus to Muju. 4 h 27 min ₩30,926. From Busan Station train to Dongdaegu, bus to Daejeon, then bus to Muju. 4 h 39 min ₩36,258. From Busan drive to Muju. 2 h 24 min ₩36,505.