Flights to Bali are plentiful, but if you are flying in from Europe or the Americas, you will undoubtedly have a flight change somewhere along the journey.
At one time, Garuda International were offering direct flights from Amsterdam to Denpasar because of civil unrest in Jakarta. Great we thought, only we flew the day after they adjusted their schedule. It was like a bus service stopping at all points in between!
If flights from Europe or the Americas to Bali seem to be coming in quite expensive, also have a look at fares to Singapore, Kuala Lumpur, Bangkok or Hong Kong as they may be worth considering. With a connecting flight to Bali, it may work out less expensive using a budget airline for the last sector and may suit your itinerary.
If you are returning to Europe or the Americas after your holiday via one of these hub airports, you could always have a little retail therapy en route!
If you're thinking of having a stopover before arriving in Bali, the best ones are Singapore, Hong Kong, Kuala Lumpur or Bangkok.
Flying from Europe, we have generally found that flights from London Heathrow and Gatwick have been the most competitive. We do not live in the U.K., but when surfing for flights, just in one example, found that we could book a flight from London to Bali via Amsterdam considerably cheaper than booking the very same flight just from Amsterdam!
A word of caution though. If you book a flight because of the price but do not intend completing all sectors, check with your airline that this is permitted, as some airlines will cancel your complete ticket and you will have not just rebook, but also repay!