The Best way to try is actually a combination of travel agent inquiry and own independent research.
Cheapest options to fly around, in most cases, are to go for low-cost airline options. But on the flip-side, do remember that there could be strict ticketing conditions for most of these airlines. Also, they do not necessarily operate from or to the cities you want to travel to. Further, full-service airlines may end up offering sudden discounts which may be a little more than these fares but with flexibility and on-board food (flights can be long to S E Asia!)
Now to your destination of Bali. The airport you want to reach is Denpasar, and the cities which you can reach economically from Delhi and connect onto further flights into Denpasar would be Singapore or Kualalumpur.
From Singapore, you can get Valuair, which is now part of Jetstar Asia and can be booked from their website: jetstarasia dot com. There is Lion Air, an Indonesian low-cost carrier which should have a direct flight as well. The Indonesian flag carrier, Garuda, flies this route too and I remember the first time I did it, I took a return flight cum hotel booking package with them, and it wasn't devastatingly expensive.
From KL, Air Asia would fly you in cheapest into Denpasar. If you do not find hopping too much to get a good price, you could try getting on a cheap ticket into Bangkok and then take the Thai Air Asia into Jakarta (capital of Indonesia), and then fly Lion Air or Wing Airlines into Denpasar. Do note that the sum of tickets, along with airport taxes if any, and expenses for food etc. for the waiting period should be worth the savings, or else just go thorugh Singapore or KL.
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