Usually the best time for singles are weekend cruises, as for the best months, probably when the prices are low, but it all depends. Try to check out roll calls for the cruises you are interested in to see who went.
I find that January is good, so if February. Then again, March can be nice and it has Spring Breakers. April is also great. May is wonderful. June might be the start of hurricane season but it is also a fine time to cruise. July isn't bad. August is wonderfully warm. September has great prices. October has even better prices. November is a wonderful way to spend Thanksgiving. December is a great way to escape the cold.
Hey: There isn't a bad time to cruise.
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"There is a great difference between being well traveled and just having been to many places." ~Me
mid January..lots of younger single people choose that time (they have low seniority for vacation bids for the "prime" months) especially from the snow belt and they have lots of Christmas $$$$ to spend
I think any month is fine for cruising depending on the destinations you want to go on your cruise. I think that you should do at least a five day cruise. Time goes by very fast and there are so many things to do.
Carnival Liberty New Year's Eve 2007
Liberty of the Seas 5/2008+11/2009
Allure 1/16/ 2011
Independence of the Seas 12/29/2013 Top-notch!