I've used the fixed fare taxi system (a shared minibus) every time I have visited Budapest - ask for the return fare. They will come and collect you from your hotel and take you back to the airport.
NB: you have to ring 24 hrs before and confirm collection.
Updates
Good tip - if you are travelling alone. Two or more people will find it cheaper to jump into one of the Zona taxis outside the airport terminal. Also fixed fare, the taxis will get you where you want to get to quicker and in more comfort.
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