You definitely will get a good discount for booking a Bermuda cruise in September. The weather on the island should be pretty close to ideal. It is prime hurricane season, but no master is going to take a cruise ship full of landlubbers (otherwise known as "passengers") anywhere near a hurricane. That's unfortunate because a storm at sea is great fun -- think of your favorite ride at the local amusement park running for a week and a half without stopping! -- but you don't get to find out. You see, some landlubbers have a penchant for turning various shades of green and creating lots of extra work for the crew under such conditions.
Seriously, hurricanes don't make it to New York very often and thus are not likely to affect embarkation and disembarkation. If there's a hurricane heading anywhere near Bermuda, you can bet that the ship will go to a destination called "Somewhere Else" to ensure that you and all of the other passengers have a wonderful cruise in spite of the adverse meteorological developments at your intended destination. In truth, this is a far better insurance policy than any resort ashore could ever give. Cruise ships have been known to divert to the Bahamas and to the Canada's Maritime Provinces since the Jones Act requires that they call at a foreign port if they call anywhere before returning to a port in the States. I'm guessing that such diversions probably occur for one week of a typical cruise season, but I don't have hard statistics on that. If you don't want to take the risk of such a diversion, book a cruise in May or early June. If you are willing to accept the risk, a September cruise should be fine.