hi if you want to live close to the hospital and take public transport,the best form of public transport would be by tram as it goes by the hospital. if you go to
Metlink - Your guide to public transport in Melbourne and Victoria and follow the links to the maps you can see what line goes past and what suburbs it travels through. also you can take your bikes on the trains so you could live further out and ride from the city 10 minutes?
hope this helps
Geoffrey