I am an Australian PR. Will Australian medicare cover me on my trips abroad (to USA/Dubai/India/Bangladesh) ?
Medicare only covers you outside Australia if the country has a reciprocal agreement with Australia.
The Australian Government has agreements with New Zealand, the United Kingdom, the Republic of Ireland, Sweden, the Netherlands, Finland, Italy, Belgium, Malta, Slovenia and Norway.
These agreements mean: Australian residents can get help with the cost of essential medical treatment when visiting these countries, and residents of these countries can get some essential medical treatments while visiting Australia.
Note that the coverage is limited to "essential" medical care only (and doesn't include repatriation).
For the countries you mentioned, you need private medical insurance (travel insurance). It often costs more if you visit the US, as the medical costs there are so high.
It's a good idea to get insurance even if you intend to visit just countries that have a reciprocal agreement, as you may need to be repatriated, or you may fall ill in a transit country.