Airport Express bus 100E is in operation between Liszt Ferenc International Airport and Deák Ferenc tér, one of Budapest’s major transport hubs, running via Kálvin tér, another important location in the city. The bus service operates around the clock, seven days a week. Please note that bus line 100E is to be used only with the 2200 HUF Airport Shuttle Bus Single Ticket. You can buy your airport shuttlebus single ticket with your bankcard using the on-board Budapest Pay&GO device and it is also available in the Budapest GO app. You can also travel with bus line 200E: it operates 24 hours a day according to the usual schedule; passengers require a valid ticket or pass (please note that the Airport Shuttle Bus Single Ticket is not accepted on bus line 200E!)
Please check this site for more information about the airport shuttle bus.