Get the 90 bus which starts in front of the new Slovak National Theater. There is no ticket machine at that stop. The trip takes approximately 34 minutes. The final stop (“Danubiana”) is a 3-minute walk from the museum. This is also where you will get the bus back to Bratislava.
Plan your trip here:
https://imhd.sk/ba/route-line/90/bd807c807f847f887f7c887f75b3817f81817c80817c8080
Ticket Types and Prices:
https://imhd.sk/ba/doc/en/20709/20709
