From Europe
KLM and TUI offer direct flights from Amsterdam Schiphol Airport to Bonaire Flamingo International Airport.
There are also daily departures to Curacao from Amsterdam Schiphol Airport offered by KLM and TUI. It's easy to travel from Curacao to Bonaire (flight time about 15 minutes) with Divi Divi Air or EZ Air. These airlines offer flights several times a day between the islands.
From Latin America
Avianca, Copa Airlines, Gol, Lan Colombia, SBA, Aserca Airlines and Surinam Airways offer flights to and from a variety of South American cities via Curacao or Aruba. From Mexico to Bonaire is available via Houston with United Airlines. Divi Divi Air and EZ Air provide inter island flights to Bonaire. 
From North America
United Airlines offers direct flights from Newark and Houston (USA) to Bonaire. Delta Airlines offers direct flights from Atlanta. American Airlines has direct flights from Miami. From Canada direct flights to Bonaire are offered by Sunwing from Toronto. Besides it's also possible to fly via Aruba or Curacao to Bonaire.
Aruba Airlines, EZ Air and Divi Divi Air provide daily service to Bonaire connecting via Aruba or Curacao.
For complete itineraries and details please contact the airlines that offer service to Bonaire.