Travel to Bruny Island itself is by ferry, but firstly how do you get to Hobart.
There are a number of flights to Hobart daily from destinations including Melbourne, Sydney, Adelaide and Brisbane. Alternatively, you can take a ferry from Melbourne with the ‘Spirit of Tasmania’ which travels daily between Melbourne and Devonport and allows visitors to bring vehicles from the Australian mainland to Tasmania. Hobart is then a 4 hour drive to south.
From Hobart to Bruny Island is normally by car, although buses do run down in that direction.
At the time of writing, the number 415 takes about an hour from Stop 7, in Davey St to the post office in Kettering, which is a short walk down to the ferry.
A word of warning abut the ferry. The Mirambeena is a covered ferry and there is a basic foot passenger lounge down some steep steps, but the other ferry is open to the elements and has no specific place for passengers.
Once on the island, there is no bus or taxi service at the moment.