How about a taxi to the Nakhonchai Air bus terminal, then a bus to Udon. (other bus companies/terminals available)
https://www.busonlineticket.co.th/booking/bangkok-to-udon-thani-bus-tickets
Edit: Some bus, train, and flight options on this website.
https://12go.asia/en/travel/bangkok/udon-thani?date=2023-05-10&people=2&direction=forward