I travel to Indonesia several times a year, and this is how I do it, though it is a bit of a twisty schedule, it gets me there finally, and at a reasonable cost....

I fly NW to Singapore: SEA-NRT-SIN

Then I spend the night in the airport, usually tucking into the airport hotel ($18 USD, book in advance, or get on waiting list for a room after 1-2 hours) for a nice nap for 6 hours), and catch a flight to Indonesia.

I almost always fly to Jakarta (CGK), but getting to Bali (DPS) is also possible.

SIN-CGK
For the Jakarta flight, I tend to take the KLM flight around 4pm, in order to get more miles (and last time an op-up to BC!), but there are many choices to Jakarta, and they are usually under $100 US (right now KLM is $76 USD return). Also with the KLM flight, I have been able to check the luggage all the way through, and they will get it to the flight for you -- just double check at the checkin desk in Singapore.

Also, AF flys into CGK too, I recall, so this flight will become an option once all of us are in the same alliance.

If I do go on the afternoon flight, I tend to go into Singapore for a nice lunch and a stroll before heading to the airport. The rapid transit is quite good.

SIN-DPS
For the Denpassar flight, the choices are Australian Airlines, Garuda and a few others. The price runs under $200 USD. You can get miles on the Garuda flight.

For booking this SIN-DPS/CGK flight, I go to zuji.com and often it is an e-ticket, so it all works fine.