Budapest’s airport is about a 30-min drive out of town. Getting there is fairly easy any time of the day. If you want to take a cab, Fötaxi is the official taxi provider at the airport (but you can call any other company you like including Taxify), while miniBUD run official airport–accommodation minibus routes. Depending on where you need to go in the city, the cab ride will cost around 8000 HUF.
You can also take the 100E bus that goes directly between Deák Square in the center of the city and the airport. The ticket for the direct bus ride is 900 HUF and you can buy the ticket on the bus or at one of the ticket machines. In general, there are about three buses in every hour, but here is the exact daily schedule:
From Liszt Ferenc Airtport (BUD) to Deák Ferenc Square (city center)
05:00am, 05:20am, 05:40am
06:00am, 06:20am, 06:40am
07:00am, 07:20am, 07:45am
08:10am, 08:30m, 08:50am
09:10am, 09:30am, 09:50am
10:10am, 10:30am, 10:50am
11:10am, 11:30am, 11:50am
12:10pm, 12:30pm, 12:50pm
1:10pm, 1:30pm, 1:50pm
2:10pm, 2:30pm, 2:50pm
3:10pm, 3:30pm, 3:50pm
4:10pm, 4:30pm, 4:50pm
5:10pm, 5:30pm, 5:50pm
6:10pm, 6:30pm, 6:50pm
7:10pm, 7:30pm, 7:50pm
8:10pm, 8:25pm, 8:40pm
9:10pm, 9:20pm, 9:40pm
10:10pm, 10:20pm, 10:40pm
11:00pm, 11:20pm, 11:40pm
12:00am, 12:20am, 12:40am
1:00am, 1:20am
From Deák Ferenc Square (city center) to Liszt Ferenc Airtport (BUD)
03:40am
04:00am, 04:20am, 04:40am
07:00am, 07:20am, 07:45am
08:00am, 08:20m, 08:40am
09:00am, 09:20am, 09:40am
10:00am, 10:20am, 10:40am
11:00am, 11:20am, 11:40am
12:00pm, 12:20pm, 12:40pm
1:00pm, 1:20pm, 1:40pm
2:00pm, 2:20pm, 2:40pm
3:00pm, 3:20pm, 3:40pm
4:00pm, 4:20pm, 4:40pm
5:00pm, 5:20pm, 5:40pm
6:00pm, 6:20pm, 6:40pm
7:00pm, 7:20pm, 7:40pm
8:00pm, 8:20pm, 8:40pm
9:00pm, 9:20pm, 9:40pm
10:00pm, 10:20pm, 10:40pm
11:00pm, 11:20pm, 11:40pm
12:00am, 12:20am, 12:40am