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 100E is only available with an Airport shuttlebus single ticket (2500 HUF) or the add on airport shuttlebus single ticket that can be purchased in addition to specified passes. You can buy your airport shuttle bus 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.