Linda,
I have sailed out of NYC, though not out of Bayonne. And, I often do the Caribbean in the shoulder season in October and November when great rates exist.
Don't worry. With the exception of a hurricane (and October is in hurricane season), your voyage will be relatively smooth. And, in the rare event a hurricane is forecast into your path, the captain will rearrange your cruise itinereary "on the fly" to stay well out of its path.
You will be in the open Atlantic, of course, so there will likely be a little higher seas than you had on your Zenith trip in the Caribbean / Gulf of Mexico. But, Constellation is nearly twice as large as Zenith, and she is equipped with very modren stabilizers. These two factors will largely negate the effects of the sea. Once you get below Charleston, you'll be sailing in warmer, calmer seas and you'll have no roblems at all.
Ted