If you google 'singles cruise' you will find some websites that specialize in singles cruises and that would give you an idea of any special cruises that would be full ship charters for singles, or perhaps a large group on a regular sailing.
Norwegian Cruise Line has taken the lead in catering to single cruisers. They have three ships currently in service that have outstanding facilities dedicated to singles - studio cabins built for one, so you don't have to pay the single supplement that often means a double fare for a single cruiser, plus a private lounge open only to those booked in the studio cabins so you can meet other singles. They also arrange dinner seatings for the singles, activities, etc.
I recently cruised on the Norwegian Getaway in one of these cabins and had a great cruise (I am married but cruised solo on this one).
Plus, Carnival has been offering some great rates for singles - they're trying to bring people back to their brand.
Best place to start is to talk to your agent and let them do the work for you. Makes life alot easier for you!
__________________ Travel Agent/Cruise Specialist w/12 yrs exp and 47 Cruises on 11 cruise lines! Favorites: Paul Gauguin - Tahiti: Uniworld River Cruises - Europe; Celebrity Solstice-class ships; Holland America - 12-nights Baltics & Russia; RCCL - 14-nights Greek Isles, Turkey, & Croatia; Holland America - 14-day Alaskan cruisetour; 10-night Canada/New England cruise; 21 days Hawaii w/7-night NCL cruise; Oceania - 25 days in Asia; more than 3 months touring Europe by train. And many all-inclusive resorts!