International airport, is there a bus to downtown Osaka near the train to Motomachi?

If you mean Kansai Airport, there is a Limujin bus that goes directly to the nearest railway Kamotomachi. From 05:45 to 22:30, the whole journey takes 70 minutes. 1550 yuan.

The bus departs from T2 terminal (1 Buy tickets at the ticket counter C outside the building, and get on at the No.8 bus stop), 15 minutes to reach T 1 terminal? (Buy tickets at the ticket counter B outside the 1 building and get on the bus at the No.7 bus stop); The bus stop in Osaka is at the Sheraton Hotel. Every day, two flights continue to go to Shinsaibashi Osaka Jal Hotel (14: 10 and 18:40). If you go back to Kansai Airport, you can take a bus here. Tickets can be purchased at the ticket vending machine at the bus stop.

Blue and white is the Mujin bus in the airport.