Star Alliance is a group of international carriers who have banded together - US Air, Air Canada, Singapore Airlines, ANA etc
The cheapest options with good connections I could find are
Air Canada to Sydney then Garuda to Bali...
There is a direct flight from Honalulu to Sydney through Hawaiian Airlines that is really cheap, but I don't know what days of the week it runs, and it arrives at night into Sydney which might muck up your transfers to Bali, but you could get all flights for around $1600AUS - add in an overnight stay in Sydney with transfers and you could be looking at a max of $1800AUS including all taxes. That is a little over $1300US including taxes. Air Canada is a little more expensive - You would prolly be looking at around $1500US including all taxes
Check out Garuda Airlines as well for availablity of flights to Bali from Sydney.
If you need a hand, let me know.