My wife and I have gone through Aruba on Continental a couple of times, most recently last January, and caught a connecting flight over. We had used ALM before and Bonaire Excel (now Bonairexpress) in January. The Continental flight arrives late Saturday about 8PM local, and Bonairexpress is showing a 10PM departing flight now so you could make that connection and get on Bonaire by around 11:30PM. The Continental return leaves Sunday morning and so the return connection is a little trickier. There is a Bonaire excel flight that departing 6AM and gets to Aruba around 7:30AM, but these flights are notoriously late on the weekend (they tried to cancel our return flight, but we insisted and they ended up flying my wife and me alone to Curacao, and expediting the loading and customs to get us on board the flight out of Aruba. Aruba is notorious for closing the flights early (we spent an extra three days our first trip after getting to the airport over an hour before the flight and finding the flight had been closed) this is due partly to the fact that you go through US Customs on Aruba and so they build in this extra requirement up front.
Another possibility that is probably more expensive than taking AA to DFW/San Juan/Bonaire would be to take Coninental into San Juan and AE to Bonaire That would get you down to two flights but last time I checked, you would have to lay over in San Juan on at least one end of the flight.
Frankly, having gone through many different routes and airlines (ALM,AA, AE, BonaireExcel, Continental) in our five previous trips enduring harrowing connections and missed planes, we are elated that Continental, our favorite airline will be starting up the direct flights in December. With the late night departure, we can drive down from Austin after work Friday, catch a nap on the plane and be there bright and early Saturday (in time to catch the madatory dive orientations that everyone does around 9AM) and are booked for February.