What area in Melbourne? I ask because I'm near the beach and it can affect your plant choices greatly. You are best to go to a local plant grower so you know they can grow in your area and the sales people know what might work best with your soil. I love the shed so I wouldn't hide it. If you plant Australian natives around it, it could look like a bush hut. Have you got young children? If so you could put the pond I front of the shed and then put up a cute fence around it so they can look but not drown. Pinterest have lots of great ideas, it's worth having a look. These photos are from Pinterest. I'm about to build on very sandy soil so I'm going to go for a native garden too. Your lucky having some large beautiful trees.

Have you considered planting outside your fence with the golden canes. (Hardy enough to re-position) Councils don't usually mind. Privacy with visual depth to them and then you can plant something more fun in your small garden space without the issue of palm roots stealing all the nutrients, A flowering vine on your mesh fence would be the fastest privacy screen.

Do you know if it is clumping or running bamboo? I've grown to love our little clump of clumping bamboo. Recently, I pruned back all the old culms, divided and transplanted it along our back fence near the cubby house. It has quickly reestablished and is doing a great job of screening out the neighbours higgle-piggle of sheds. I can see that yours needs some pruning ton thin it out and show off the stems, but you might find that you can create an attractive, instant and cost effective screen to be a uniform backdrop to some new feature plants in pots (bamboo can look good in a classic garden but I have to agree that bamboo and roses aren't the best combination)

Hi Emma, You need a canopy of tall plants to create a tropical Balinese garden, palms for shade, large leaf plants bright cordyline , helliconia, bromeliads, ferns , water features to give that tropical lush look, you are on the right track just need to mass plant to achieve the desired effect