What's inexpensive? It is doable but back thru Miami twice during the trip. Total cost for the main flights is $1164. Plus there would be about $500 in add-on costs - see below:
From Bonaire you'd need fly over to Curacao via Insel, Divi, or the other local airline. The Insel flight is $42 one way. Plus the Bonaire departure tax - $36?
And there's also a Curacao departure tax you'd have to pay the next day unless AA includes it - they did for us.
To take advantage of the cheapest flight option, you'd have to go over the night before for the 755AM departure. To get a 10:30AM departure, the fare goes to $1707. There used to be an average looking airport hotel - not sure if it's still there.
Otherwise something in town like the Plaza is about $70/nt. There's also a new Marriott Renaissance but I'm guessing it's more. There's also a Hilton and a Marriott in Piscadera Bay - they'd be slightly closer - but may cost more as that's a resort area.
From Curacao you fly to SAP (San Pedro Sula) on mainland Honduras and then take a local flight to Utila - about $120 r/t IIRC - then back to SAP and on to Providenciales.
You'd also have to stay overnight both ways to get to/from San Pedro as flights to/from Utila stop when it gets dark. I've never been to SAP but have read hotel suggestions in the Bay Islands forum. Who are you staying with on Utila? maybe they can help. There's a travel agent mentioned frequently in the forum that specializes in local Utila travel connections.
From SAP it's on to Providenciales and then back to Ft. Lauderdale.
Here's a sample itinerary with the three flights a week apart.
7:55 am Depart Willemstad (CUR)
Arrive San Pedro Sula (SAP) 7:20 pm Sun 11-Jul
Duration: 13hr 25mn
American Airlines American Airlines 934 / 949
Connect in Miami (MIA)
7:15 am Depart San Pedro Sula (SAP)
Arrive Providenciales (PLS) 8:40 pm Sat 17-Jul
Duration: 11hr 25mn
American Airlines American Airlines 944 / 625
Connect in Miami (MIA)
3:30 pm Depart Providenciales (PLS)
Arrive Fort Lauderdale (FLL) 10:12 pm Sat 24-Jul
Duration: 6hr 42mn
UNITED 1632 operated by US AIRWAYS1632 / UNITED 1899 operated by US AIRWAYS1899
Connect in Charlotte (CLT)
Another option is to look at Insel Air from Bonaire to Miami. It might be possible to save some money that way - Insel Air doesn't show up on the big booking sites like Expedia. I also didn't price MIA as a final destination as I assumed you'd want to land in Ft. Lauderdale.
The easy way to plan this is to go onto Expedia or Travelocity, select the multiple destinations option and fill in your details.
hth,