LA to Bali is a tricky ticket to find a cheap flight on mainly as there are so many different ticketing options for routing, in addition you also have regional flights that you can look at to reduce the total ticket price of your international flight from LAX to DPS.
The way most people do it, which is the easiest and even sometimes the cheapest, is to go to your regular carrier and see what rate they are offering; this is a 10000 mile flight, so you can figure the frequent flyer miles are worth $100 to a $150, if you are someone that flies often. We use Star Alliance partners with United Airlines and we look first on Sidestep and Kayak to see what the rates are in general and then go to the airlines direct. United for instance has a policy that we have never tried that says that they will be anybody else's prices using United Airlines.

The other things that you should be looking at is can you fly to any of the major Asia hub cites like Bangkok, Singapore, Hong Kong and a non major hub I personally would look at would be Manila, and jump a regional jet Like Air Asia, Jet Star Asia, Tiger air or Cebu Pacific looking to go direct to Bali or route through KL, Singapore or Batam Indonesia.
Batam has a couple of local Indonesian airlines and within Indonesia they are almost always cheapest, cheaper even that Air Asia! Lion Air usually is the best that we have found with rates round trip for $200.
Another thing to be aware of is airport taxes which in Asia can add up quickly if they are not included in the air ticket price. Phnom Penh is $25 Bali is around $17 and Bangkok and Singapore are included in the price. One clue to look for is if there is a big difference in price on the same flight going in the opposite direction. This is not fool proof as both may or may not include and the fares will look similar and you might find yourself paying more than you planned.