American Airlines has round-trip flights from Dallas (DFW) to Nassau, Bahamas (NAS) for $372, NONSTOP. Flights November, December, January, February, March, April, May, July, and August. Weekends available. Origin/Destination reversible. Dates over Christmas (Dec 20 – Dec 27) are available.
A Carry-on bag and also a personal item is allowed for free on American. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.