The best time depends upon where you are thinking of chartering. The high seasons for the Caribbean and Mediterranean are directly opposed. The busiest time in the Caribbean is from Xmas to the end of March.
Winter is also the time of year when the wind blows the strongest in the Caribbean.
April, May, and June are a bit less busy, and winds are more pleasant. Summertime of year that is favored by many.
July and August, as well as November, are my favorite time of year in the Caribbean. The winds can be light, and the sun can be intense during these months. The days of very light winds make for some beautiful diving and snorkeling. I have gone a whole week in these months with only seeing a hand full of other boats. The rates for bareboats can be cheaper than in the prime months. The months of September and October are the two months that the Caribbean is likely to see a hurricane.
Hurricane season does not mean that you can’t take bareboats in these months but do have trip insurance. If a hurricane is on the horizon, your bareboat company will call you back to base, take care of the boat for you with advice on hotels, shelters, or plane changes. These months have exciting weather. Typically you get 2 or 3 days of dead flat weather; then, a substantial electrical storm passes that will last a half day then go back to dead flat seas — not a good time to sail but a great time to rent a powerboat. If you are a scuba diver, then this is a perfect time to boat. Super low bargain prices can be had at this time, like pay for seven nights and get 10.
In my books, the best time to bareboat is when I have the time!