The Bastion Beautiful Bedrooms is located in the historic part of Budapest right in the city center, where the acient Bastion wall was standing.You can still see a part of it.

How to get here from the Budapest Ferihegy Airport:

Shuttle bus (mini bus): 
The shuttle bus goes from Budapest Airport to any point in Budapest or from any point in Budapest to the airport. Tickets can be purchased in the offices, located in the  terminals. The offices are at your service from 0 am till 12 pm in both terminals. The price is 13 Euro to anywhere in the city.

Zona Taxi:
Ask the information desk for Zona Taxi. They give you a transfer anywhere, for a fixed price. The fares (in your case will be 23 Euro) are the maximum which zona service will be allowed to charge in each zone for a journey. The ride will be metered and if it shows a lower fare, then the passengers will only pay the lower price.

Public Transfer:
Budapest Airport is relatively well accessible also by public transportation. Passengers are taken by a direct bus service from Terminal 1 and 2, called the bus 200 to Kőbánya-Kispest metro station (tickets from the driver).
This service is more flexible for the passenger traffic at the airport: it is larger so bigger luggages can be transported, it operates more frequently, and it operates for longer hours providing a link between the city and the airport even after midnight and early dawn.
By the Metro number M3 (blue line) you can reach Kálvin square in less then 20 minutes (tickets at the station Kőbánya-Kispest). As you come up, you go to Kecskeméti street under the walkway of the hotel Mercure building and make a left turn into the first street called Bástya. Walk two blocks and you will find on your right the number 10.