There are direct flights on United from Houston and Newark, and on Delta from Atlanta.
These flights are usually on the weekends.
The best way to find them is to look for one leg at a time, then enter both legs as a round trip because if you search for a round trip and put the wrong number of days it will give you wrong result or no result.
I usually use

If you need to fly mid-week for some reason, you can fly to Curacao on several airlines Jetblue and AA are two I know of.
Then take to Bonaire. This isnt as bad as sounds because Divi flys several times a day and it’s a cheap 20 minute flight. Divi wont show up on your flight searches.
If none of the Divi flights work I can also help you arrange a private plane. Also not as bad as it sounds. What is bad is Insel Air so avoid that. Of course its easier to fly directly to Bonaire so fly on the weekends if you can.

Also, if your schedule is flexible, I would wait til the wind report comes out before booking, so if no wind, you can reschedule. The prices do not increase significantly if you book last minute. Sometimes the higher classes will sell out but its better to be stuck in coach than stuck in Bonaire when theres no wind. Its usually windy almost every day from Jan til Aug, but when the wind stops, it usually doesnt come back for a few days so you dont wanna catch one of those weeks.