When should I buy airplane tickets to St. Lucia (from US)?

I am not sure why you could not find any flights. There are obviously regular flights from US destinations arriving in St.Lucia.

Checking on one of the arriving airlines, AA, I went to their site directly and tried to book a flight in November, and got tons of results. Maybe you want to try that way instead of going through Bing or Google.

In general, when booking in holiday seasons, you might find more packages that are offered together with the hotel, since a lot of agents might book bulk-seats with bulk-hotel beds and sell them together. The longer you wait, the less non-package airline seats will be available.

I think in your case two elements are playing and the crux is not really when to book.

First of all, as already pointed out by Nate Eldrege, you probably searched with the "wrong airports". Saint Lucia has more than one airport and so has Washington DC. If you pick an unfortunate combination you will probably end up with ... unfortunate routings. Saint Lucia is quite small and the airports are only 60 kilometers apart from each other (a 1h00 to 1h30 drive).

I usually use the Matrix Airfare Search to explore the possible routings. Anyway, this engine does not allow you to to a booking. You will have to go to a travel agency or to a specialized website. With Matrix Airfare Search, you can for Washington DC and Saint Lucia use the "All Airports" option as shown below. The search engine will then have a wider scope. In addition you can use the "Nearby" feature. This will extend the search to other airports you sepcify. In the case of Washington DC, Baltimore would be an obvious candidate.

Second, November is probably not the "best" period to go to Saint Lucia. It is not the most busy period and there may still be some cyclones. In the high tourist season from December to April there will probably be more options, including charter flights.

Were you searching for SLU as your destination airport? According to Wikipedia, that is a small secondary airport, and it's not surprising that getting there would require a convoluted itinerary. But getting from the US to St. Lucia via Europe is ridiculous.

The main international airport on St. Lucia is Hewanorra, whose code is UVF, and it has lots of nonstop flights to the US. Searching for flights from WAS (or DCA or IAD) to UVF turns up lots of reasonable looking results.