Mmmm.
That's a small budget, even by Bali standards. It's the sort of price reasonably affluent locals might pay, but as a foreigner, you already have the "I am an ATM" sign blazing in neon lights on your forehead and would be extremely lucky, IMO, to get local price.
Your budget works out as follows, assuming 8,400 rupiah to 1 AUD:
$50AUD  to $100 AUD per week       Â
i.e. 420,000 to 840,000 rupiah per week     Â
i.e. 21,840,000 to 43,680,000 rupiah per annum
i.e. 1,820,000 to 3,640,000 rupiah per month
I have seen the occasional house (Bali local style - no pool, no aircon)for as low as 45 million a month in the northern part of the Kerobokan area, but these are rare, and not in areas generally frequented by expats. Anything near a beach carries a premium price, even in remote areas.
You could also look for a Kost (boarding house) where you get one room, unfurnished. The good ones have a Bali-style 'bathroom' in an alcove of the one main room. The poorer ones have a communal bathroom shared by all residents. As an example, next door to my villa is a complex of near new, modern-style kost rooms. One room, private bathroom, air-conditioning. Stacked next to each other like motel units. Price, 3 to 3.6 million rupiah per month.
My personal opinion (others may disagree) is that you only have two choices:
1) Live in the boondocks where you will be up to 8 hours travel away from any Western-standard medical assistance, have little personal security and won't have many of the comforts many of us take for granted. However, is you speak passably good Bahasa and establish an excellent relationship with the local banjar, you might make a go of it.
2) Search for a homestay situation. There are some lovely Indo families who will take in homestay guests at a reasonable price. Some report they become 'part of the family', BUT remember that in Bali, being even an honorary part of the family carries its own responsibilities, expectations and obligations. These are often called upon if someone in your host's group gets sick, has an accident, or needs something - and your response is often expected to be financial.
Just be careful. Your dream is a wonderful one - although somewhat difficult to attain on the budget you mention. Remember to allow for all the other normal expenses too - eg electricity is about 3 times as expensive as in Oz, and internet access could cost you nearly 1,000,000 per month for a slow, unreliable service. Then there's the cost of a visa for expat residents - expensive as hell.
But it CAN be done if you plan carefully and have some money behind you for those inevitable emergencies.
Best of luck, Vyt