From North America

Continental serves Bonaire directly from mainland USA on overnight flights from Houston  (Friday night) and Newark (Saturday night), and adds more flights on occasional basis in high-season periods.

Delta flies directly from Atlanta weekly on Saturday.
It will commence weekly non-stop flights from New York JFK (also on Saturdays) starting December 20, 2008.

American Airlines operates 3 weekly flights from San Juan, Puerto Rico to Bonaire, with originating gateways from many major U.S. cities. 

It is also possible to connect with any of the major airlines through Aruba (Air Canada, American Airlines, Continental, Jetblue, United Airlines, US Airways) or Curaçao (American Airlines, Air Jamaica, Continental)

From Aruba, one can connect via Tiara Air or Dutch Antilles Express.

From Curaçao, one can connect via Dutch Antilles Express, Insel Air or Divi Divi Air.

From Europe

KLM operates directly from Amsterdam to Bonaire 7 times a week; on 6 of these flights, Bonaire serves as a stopover on the way to Quito, Ecuador. The flight on Thursdays however, flies Amsterdam-Bonaire directly and returns with a stopover on Aruba.

Arkefly operates directly from Amsterdam once a week (on Saturdays). This flight returns with a stopover on Curaçao.

It is also possible to fly to Curaçao from Amsterdam (KLM, Arkefly, Martinair), and connect from there to Bonaire on Dutch Antilles Express, Insel Air or Divi Divi Air.