Bermuda cruises from NY are generally no problem for Celebrity to sell out. You can save some money by sailing the first cruise or two in the Spring or the last cruise or two in the Fall. Otherwise you are cruising peak time, in a busy market, with only a handful of smaller ships serving a very popular destination. You will not find the steep
discounts as in off season Caribbean or Alaska. We have done the trip twice. Paid a little less than you are being quoted, but not much. If you are coming from the NY area , you have to take into account no airfare, no precruise hotel, travel time etc.
In addition, for the 3 and a half days that you are in Bermuda (day and night) the ships' shops and casino are not open and many people leave the ship at night to drink at the pubs so the bar revenues are lower as well. This is one cruise where the fare (not the extras ) has to PAY for the cruise.
Shop a round a bit, but I don't think you will find any really deep discounts and July is the absolute peak for Bermuda prices.
I highly recommend the cruise. Bermuda is my favorate cruise destination.