These discount deals to this sandy Atlantic archipelago are available daily starting in mid-September through the end of April 2019, although some months in 2019 travel is only available Monday through Thursday. No minimum stay required.
As an example, searching on the Delta, I found seats departing DCA on Wednesday, September 26, and returning from NAS on Monday, October 1, 2018. Fares are wide open at this price and relatively easy to find on any booking site. Tickets book into the basic economy fare buckets, but on American and Delta that still entitles you to a standard sized carry-on bag, whilst United will only allow you a small personal item. Checked baggage will cost additional.
Need a room in Nassau? Here's what's available for the mentioned dates on Hotelwatchdog.