The best prices for transatlantic crossings are going to be repositioning cruises.
In the Spring, cruise lines move their ships from the Caribbean to Europe and they offering some very good deals.
Prices shown are per person and do not include taxes. A single will normally pay double the price. Now here's the catch; an advertise price consists of two fares - the cruise fare and the port fees. When traveling alone, some cruise lines will double the cruise fare but not the port fees. Some cruise lines, like NCL for example, will double the cruise fare and double the port fees. Just their way of making more profit because they do not need to double the port fees. (The ports charge these fees based on the number of people, not the number of cabins.)
As for finding another single to share a cabin, this use to be more prevalent than it is now, what with all the litigation problems. So it's always best to find someone to go with you or just bite the bullet and go by yourself.
But you'll definitely want to check out the transatlantic repositioning cruises as you'll find some good rates.