We were a provided travel suggestions from our agent when we went to Budapest last year.
He recommended for "private transfers" Romulus Travel. http://romulus-travel.com
Bolt is the transportation/ride app that many use in Hungary
We flew in @1:30am, taxis were still running to get us to the Marriott. Taxi booth check-in and then get in the cue. Used apple pay for fare. Piece of cake!