The primary gateway to Indonesia is the Sukarno-Hatta International Airport of Jakarta (also known as Cengkareng CKG), but there are increasingly more international airlines that offer direct flights to Bali. From Jakarta, Garuda Indonesia and Sempati Air have around a dozen departure times to Bali. Internationally, Garuda also has direct flights from Singapore, Hong Kong, and a number of Australian cities; as well as flights from Los Angeles, Amsterdam, and other European cities.
Qantas Airlines of Australia provides direct flights from a number of Australian cities as well as a number of European cities (e.g. London). Air New Zealand will also take you from Auckland to Bali. KLM of the Netherlands is one of the first international airlines to have an international flight to Bali, and it will take you from many cities in Europe, notably Amsterdam, to Bali. Lauda Air, Lufthansa Airlines and Air France can also assist you to escape from Europe.
From Asia, direct flights from Bangkok, Singapore, Kuala Lumpur, and Hong Kong are readily available from Garuda Indonesia, Thai Airlines, Singapore Airlines, and Malaysia Airlines.