When I visited BUD a couple of years ago, the only ATM at the airport was empty! And they don't use Euros there, either.
I got lucky since I had and extra US$100 in my billfold for just these events. I exchanged US$ -> HUF at the exchange window and even got a fair rate.
Then I asked about getting on the next hotel (shared ride) shuttle and was told that the next 6 vans were sold out! So I got a taxi and paid an OK fare to my hotel.
Enjoy Budapest. The food is pretty good (and cheap), too.