I suggest you post this in the single cruisers area, which has its own message boards. And, e-mail CruiseMates' singles editor, Pat Hagen (firstname.lastname@example.org), for any advice.
You didn't mention your age range, but Crystal Cruises has the best single occupancy rate, around 15% above double occupancy fares. Singles stay in outside cabins. And, with all the discounts around, you can probably save a lot of money on top of this. There are lots of singles aboard this ship, guest lecturers and enticing itineraries. The food and service are the best.
But Pam can fill you in on other ships as well.