There is a round trip airport shuttle that you can book ahead online. The booking website is different from 2015, but it looks like the service and price are similar. You can book for your round trip to save on fare — also if you want to coordinate with others coming in at the same time you’ll save a little with more passengers on the reservation.
GO TO: www.minibud.hu You can translate to English.
You will need your flight number and arrival time (also for departing flight if booking round trip shuttle). To fill in hotel location start entering the street name (Zólyomi út 6) and the complete hotel name and address will populate. You pay with credit card. Print your confirmation when it comes to your email address and have it with you on arrival.
There is also an option of adding on a Budapest Card which covers some tourist transportation and attractions. And admission on a Hop On Hop Off siteseeing bus is another option. You can get these for various numbers of days, and it looks like you don’t have to lock them in for a certain days. I don’t know how the package price compares to buying them on the street.
If the shuttle service works the same as last time, you may buy your shuttle passes from a station in the arrival hall. You can pay by credit card or Euros. If you pay with Euros, change is in Forent (local currency).
After exiting baggage claim there is a shuttle station where they scan the bar code on your receipt and give you a ticket. You can see on a monitor when your shuttle arrives and you will find the van outside where the driver takes your ticket. It is about a 45 minute ride to the hotel.