Or drop by Chat and Browse and rent a phone. From what I understand that is the least cost way if you intend to use it.
Fuhgettabout AT&T or Verizon!! The cheapest option to call home from Bonaire is using SKYPE. Nothing beats it, (assuming you have an internet connection where you're staying)! Bring your laptop, a headset & you're good to go.
While both of these are options viable, if not without their own logistical problems (computer running Skype, WIFI/Internet connection available when/where you wish to converse/expect to be called, etc.) neither answered the OP's original question regarding availability of cell service on Bonaire.