Map from Google - Bermuda

The archipelago of Bermuda has a very mild climate, due to the influence of the Gulf Stream, but it is not a tropical paradise, at least in winter.
The annual precipitation is around 1,400 mm; the rains are fairly evenly distributed throughout the year, because the flow of weather fronts in winter is replaced by the tropical rains in the summer months. Anyway, the least rainy months are April and May, while the rainiest month is October.
Here is the average precipitation in Hamilton, the capital.
Average precipitation - Hamilton
HamiltonJanFebMarAprMayJunJulAugSepOctNovDecYear
HamiltonJFMAMJJASONDY
Prec. (mm)13011511090851301151301301601051151410
Days1312118711101212131113133

In winter, from November to March the temperatures are very mild, with lows around 15/17 °C and highs around 20/22 °C. Sometimes the weather is nice and the sun shines, but this kind of weather is not always guaranteed: in fact there is no shortage of rainfall, so much so that there are about 11/13 rainy days per month, and windy days as well.
In summer, Bermuda is hot and muggy, with highs around 30 °C in July and August, even though the heat is tempered by the breezes. There are about 10/12 days of rain per month, but usually in this season the rain comes in the form of short and intense showers and thunderstorms, which break out in the evening and do not affect much the sunshine amount.
Here are the average temperatures.
Average temperatures - Hamilton
HamiltonJanFebMarAprMayJunJulAugSepOctNovDec
HamiltonJFMAMJJASOND
Min (°C)161616172023242524211917
Max (°C)202020222427293029262421

In addition, in summer the archipelago can be hit by hurricanes. The hurricane season runs from June to November. In general, hurricanes do not hit Bermuda at the peak of their violence, because the ocean at this latitude is less warm than the Gulf of Mexico, however, they can still bring strong winds and heavy rains.

The hours of sunshine are not many from November to March, when there are several cloudy days, while from April to September, the percentage of sunshine is quite good.

Bermuda

The sea is cool in winter, when the water temperature is around 19/20 °C; the sea becomes pleasantly warm from June to October or November, with a spike in August, when the temperature reaches 28 °C.
Sea temperature - Bermuda
BermudaJanFebMarAprMayJunJulAugSepOctNovDec
BermudaJFMAMJJASOND
Sea (°C)202019202124272827252322

When to go

Having a favorable climate, Bermuda can be visited all year round, in winter to relax, play sports or explore nature, in summer for swimming and sunbathing.
In summer, however, there's some risk of hurricanes.
All in all, April and May seem to be the best months, especially May, at least with regard to weather conditions, since it's still a bit cool for swimming: the air daytime temperature is around 24 °C, while the sea temperature is around 21 °C.

What to pack

From December to April: light clothes, but also sweatshirt or sweater, jacket and umbrella.
From June to September: summer clothing, a light sweatshirt and a light raincoat for thunderstorms.